diff --git a/Marlin/Conditionals_post.h b/Marlin/Conditionals_post.h
index ff997ce109..709e87e645 100644
--- a/Marlin/Conditionals_post.h
+++ b/Marlin/Conditionals_post.h
@@ -39,20 +39,31 @@
   #define Z_CENTER float((Z_MIN_POS + Z_MAX_POS) * 0.5)
 
   /**
-   * CoreXY and CoreXZ
+   * CoreXY, CoreXZ, and CoreYZ - and their reverse
    */
-  #if ENABLED(COREXY)
-    #define CORE_AXIS_1 A_AXIS // XY from A + B
-    #define CORE_AXIS_2 B_AXIS
-    #define NORMAL_AXIS Z_AXIS
-  #elif ENABLED(COREXZ)
-    #define CORE_AXIS_1 A_AXIS // XZ from A + C
-    #define CORE_AXIS_2 C_AXIS
-    #define NORMAL_AXIS Y_AXIS
-  #elif ENABLED(COREYZ)
-    #define CORE_AXIS_1 B_AXIS // YZ from B + C
-    #define CORE_AXIS_2 C_AXIS
-    #define NORMAL_AXIS X_AXIS
+  #define CORE_IS_XY (ENABLED(COREXY) || ENABLED(COREYX))
+  #define CORE_IS_XZ (ENABLED(COREXZ) || ENABLED(COREZX))
+  #define CORE_IS_YZ (ENABLED(COREYZ) || ENABLED(COREZY))
+  #define IS_CORE (CORE_IS_XY || CORE_IS_XZ || CORE_IS_YZ)
+  #if IS_CORE
+    #if CORE_IS_XY
+      #define CORE_AXIS_1 A_AXIS
+      #define CORE_AXIS_2 B_AXIS
+      #define NORMAL_AXIS Z_AXIS
+    #elif CORE_IS_XZ
+      #define CORE_AXIS_1 A_AXIS
+      #define NORMAL_AXIS Y_AXIS
+      #define CORE_AXIS_2 C_AXIS
+    #elif CORE_IS_YZ
+      #define NORMAL_AXIS X_AXIS
+      #define CORE_AXIS_1 B_AXIS
+      #define CORE_AXIS_2 C_AXIS
+    #endif
+    #if (ENABLED(COREYX) || ENABLED(COREZX) || ENABLED(COREZY))
+      #define CORESIGN(n) (-(n))
+    #else
+      #define CORESIGN(n) (n)
+    #endif
   #endif
 
   #define IS_SCARA (ENABLED(MORGAN_SCARA) || ENABLED(MAKERARM_SCARA))
diff --git a/Marlin/Configuration.h b/Marlin/Configuration.h
index b70b57dbbb..4610c4f945 100644
--- a/Marlin/Configuration.h
+++ b/Marlin/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/Marlin_main.cpp b/Marlin/Marlin_main.cpp
index b1a5b6c74a..6e6c1d3813 100755
--- a/Marlin/Marlin_main.cpp
+++ b/Marlin/Marlin_main.cpp
@@ -3078,7 +3078,7 @@ inline void gcode_G4() {
       SERIAL_ECHOLNPGM("Delta");
     #elif IS_SCARA
       SERIAL_ECHOLNPGM("SCARA");
-    #elif ENABLED(COREXY) || ENABLED(COREXZ) || ENABLED(COREYZ)
+    #elif IS_CORE
       SERIAL_ECHOLNPGM("Core");
     #else
       SERIAL_ECHOLNPGM("Cartesian");
diff --git a/Marlin/SanityCheck.h b/Marlin/SanityCheck.h
index 3cd9adeb6b..ebb1008002 100644
--- a/Marlin/SanityCheck.h
+++ b/Marlin/SanityCheck.h
@@ -57,8 +57,8 @@
   #error "Thermal Runaway Protection for hotends is now enabled with THERMAL_PROTECTION_HOTENDS."
 #elif DISABLED(THERMAL_PROTECTION_BED) && defined(THERMAL_PROTECTION_BED_PERIOD)
   #error "Thermal Runaway Protection for the bed is now enabled with THERMAL_PROTECTION_BED."
-#elif ENABLED(COREXZ) && ENABLED(Z_LATE_ENABLE)
-  #error "Z_LATE_ENABLE can't be used with COREXZ."
+#elif (CORE_IS_XZ || CORE_IS_YZ) && ENABLED(Z_LATE_ENABLE)
+  #error "Z_LATE_ENABLE can't be used with COREXZ, COREZX, COREYZ, or COREZY."
 #elif defined(X_HOME_RETRACT_MM)
   #error "[XYZ]_HOME_RETRACT_MM settings have been renamed [XYZ]_HOME_BUMP_MM."
 #elif defined(SDCARDDETECTINVERTED)
@@ -644,8 +644,23 @@
 #else
   #define COUNT_KIN_7 COUNT_KIN_6
 #endif
-#if COUNT_KIN_7 > 1
-  #error "Please enable only one of DELTA, MORGAN_SCARA, MAKERARM_SCARA, COREXY, COREXZ, or COREYZ."
+#if ENABLED(COREYX)
+  #define COUNT_KIN_8 INCREMENT(COUNT_KIN_7)
+#else
+  #define COUNT_KIN_8 COUNT_KIN_7
+#endif
+#if ENABLED(COREZX)
+  #define COUNT_KIN_9 INCREMENT(COUNT_KIN_8)
+#else
+  #define COUNT_KIN_9 COUNT_KIN_8
+#endif
+#if ENABLED(COREZY)
+  #define COUNT_KIN_10 INCREMENT(COUNT_KIN_9)
+#else
+  #define COUNT_KIN_10 COUNT_KIN_9
+#endif
+#if COUNT_KIN_10 > 1
+  #error "Please enable only one of DELTA, MORGAN_SCARA, MAKERARM_SCARA, COREXY, COREYX, COREXZ, COREZX, COREYZ, or COREZY."
 #endif
 
 /**
@@ -662,8 +677,8 @@
 #if ENABLED(DUAL_X_CARRIAGE)
   #if EXTRUDERS == 1
     #error "DUAL_X_CARRIAGE requires 2 (or more) extruders."
-  #elif ENABLED(COREXY) || ENABLED(COREXZ)
-    #error "DUAL_X_CARRIAGE cannot be used with COREXY or COREXZ."
+  #elif CORE_IS_XY || CORE_IS_XZ
+    #error "DUAL_X_CARRIAGE cannot be used with COREXY, COREYX, COREXZ, or COREZX."
   #elif !HAS_X2_ENABLE || !HAS_X2_STEP || !HAS_X2_DIR
     #error "DUAL_X_CARRIAGE requires X2 stepper pins to be defined."
   #elif !HAS_X_MAX
diff --git a/Marlin/endstops.cpp b/Marlin/endstops.cpp
index 53e8b209e5..653e0753a9 100644
--- a/Marlin/endstops.cpp
+++ b/Marlin/endstops.cpp
@@ -268,7 +268,7 @@ void Endstops::update() {
 
   #endif
 
-  #if ENABLED(COREXY) || ENABLED(COREXZ)
+  #if CORE_IS_XY || CORE_IS_XZ
     // Head direction in -X axis for CoreXY and CoreXZ bots.
     // If DeltaA == -DeltaB, the movement is only in Y or Z axis
     if ((stepper.current_block->steps[CORE_AXIS_1] != stepper.current_block->steps[CORE_AXIS_2]) || (stepper.motor_direction(CORE_AXIS_1) == stepper.motor_direction(CORE_AXIS_2))) {
@@ -298,11 +298,11 @@ void Endstops::update() {
             #endif
           }
       }
-  #if ENABLED(COREXY) || ENABLED(COREXZ)
+  #if CORE_IS_XY || CORE_IS_XZ
     }
   #endif
 
-  #if ENABLED(COREXY) || ENABLED(COREYZ)
+  #if CORE_IS_XY || CORE_IS_YZ
     // Head direction in -Y axis for CoreXY / CoreYZ bots.
     // If DeltaA == DeltaB, the movement is only in X or Y axis
     if ((stepper.current_block->steps[CORE_AXIS_1] != stepper.current_block->steps[CORE_AXIS_2]) || (stepper.motor_direction(CORE_AXIS_1) != stepper.motor_direction(CORE_AXIS_2))) {
@@ -320,11 +320,11 @@ void Endstops::update() {
           UPDATE_ENDSTOP(Y, MAX);
         #endif
       }
-  #if ENABLED(COREXY) || ENABLED(COREYZ)
+  #if CORE_IS_XY || CORE_IS_YZ
     }
   #endif
 
-  #if ENABLED(COREXZ) || ENABLED(COREYZ)
+  #if CORE_IS_XZ || CORE_IS_YZ
     // Head direction in -Z axis for CoreXZ or CoreYZ bots.
     // If DeltaA == DeltaB, the movement is only in X or Y axis
     if ((stepper.current_block->steps[CORE_AXIS_1] != stepper.current_block->steps[CORE_AXIS_2]) || (stepper.motor_direction(CORE_AXIS_1) != stepper.motor_direction(CORE_AXIS_2))) {
@@ -390,7 +390,7 @@ void Endstops::update() {
           #endif // !Z_MIN_PROBE_PIN...
         #endif // Z_MAX_PIN
       }
-  #if ENABLED(COREXZ)
+  #if CORE_IS_XZ || CORE_IS_YZ
     }
   #endif
 
diff --git a/Marlin/example_configurations/Cartesio/Configuration.h b/Marlin/example_configurations/Cartesio/Configuration.h
index e34be9f4a2..6ba809172c 100644
--- a/Marlin/example_configurations/Cartesio/Configuration.h
+++ b/Marlin/example_configurations/Cartesio/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/Felix/Configuration.h b/Marlin/example_configurations/Felix/Configuration.h
index 923cd3a41f..bde82b2931 100644
--- a/Marlin/example_configurations/Felix/Configuration.h
+++ b/Marlin/example_configurations/Felix/Configuration.h
@@ -390,9 +390,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/Felix/DUAL/Configuration.h b/Marlin/example_configurations/Felix/DUAL/Configuration.h
index 0a202134f1..e4f92618bd 100644
--- a/Marlin/example_configurations/Felix/DUAL/Configuration.h
+++ b/Marlin/example_configurations/Felix/DUAL/Configuration.h
@@ -390,9 +390,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/Hephestos/Configuration.h b/Marlin/example_configurations/Hephestos/Configuration.h
index cae5d1e015..3d033f95c0 100644
--- a/Marlin/example_configurations/Hephestos/Configuration.h
+++ b/Marlin/example_configurations/Hephestos/Configuration.h
@@ -400,9 +400,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/Hephestos_2/Configuration.h b/Marlin/example_configurations/Hephestos_2/Configuration.h
index 64f39a2f0d..79a797df58 100644
--- a/Marlin/example_configurations/Hephestos_2/Configuration.h
+++ b/Marlin/example_configurations/Hephestos_2/Configuration.h
@@ -402,9 +402,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/K8200/Configuration.h b/Marlin/example_configurations/K8200/Configuration.h
index a76ad5ea92..ec46a33fa2 100644
--- a/Marlin/example_configurations/K8200/Configuration.h
+++ b/Marlin/example_configurations/K8200/Configuration.h
@@ -438,9 +438,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/K8400/Configuration.h b/Marlin/example_configurations/K8400/Configuration.h
index ab24c1b039..35ae51196c 100644
--- a/Marlin/example_configurations/K8400/Configuration.h
+++ b/Marlin/example_configurations/K8400/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/K8400/Dual-head/Configuration.h b/Marlin/example_configurations/K8400/Dual-head/Configuration.h
index ca4cff7cbe..5d1c84c45c 100644
--- a/Marlin/example_configurations/K8400/Dual-head/Configuration.h
+++ b/Marlin/example_configurations/K8400/Dual-head/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/RepRapWorld/Megatronics/Configuration.h b/Marlin/example_configurations/RepRapWorld/Megatronics/Configuration.h
index 726aff69cc..bc96cb8820 100644
--- a/Marlin/example_configurations/RepRapWorld/Megatronics/Configuration.h
+++ b/Marlin/example_configurations/RepRapWorld/Megatronics/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/RigidBot/Configuration.h b/Marlin/example_configurations/RigidBot/Configuration.h
index 54e9d86db5..d1c2334e70 100644
--- a/Marlin/example_configurations/RigidBot/Configuration.h
+++ b/Marlin/example_configurations/RigidBot/Configuration.h
@@ -405,9 +405,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/SCARA/Configuration.h b/Marlin/example_configurations/SCARA/Configuration.h
index 2ef2772447..6f72476cbf 100644
--- a/Marlin/example_configurations/SCARA/Configuration.h
+++ b/Marlin/example_configurations/SCARA/Configuration.h
@@ -423,9 +423,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/TAZ4/Configuration.h b/Marlin/example_configurations/TAZ4/Configuration.h
index be7d9d25f9..6f4afcf377 100644
--- a/Marlin/example_configurations/TAZ4/Configuration.h
+++ b/Marlin/example_configurations/TAZ4/Configuration.h
@@ -429,9 +429,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/WITBOX/Configuration.h b/Marlin/example_configurations/WITBOX/Configuration.h
index b1cba78d82..fc5f81503a 100644
--- a/Marlin/example_configurations/WITBOX/Configuration.h
+++ b/Marlin/example_configurations/WITBOX/Configuration.h
@@ -400,9 +400,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/adafruit/ST7565/Configuration.h b/Marlin/example_configurations/adafruit/ST7565/Configuration.h
index 837b6c2684..aa2079865c 100644
--- a/Marlin/example_configurations/adafruit/ST7565/Configuration.h
+++ b/Marlin/example_configurations/adafruit/ST7565/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/delta/biv2.5/Configuration.h b/Marlin/example_configurations/delta/biv2.5/Configuration.h
index cd16f383c3..93b8c99499 100644
--- a/Marlin/example_configurations/delta/biv2.5/Configuration.h
+++ b/Marlin/example_configurations/delta/biv2.5/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 //===========================================================================
 //============================== Delta Settings =============================
diff --git a/Marlin/example_configurations/delta/generic/Configuration.h b/Marlin/example_configurations/delta/generic/Configuration.h
index 3ace6e84ca..38ac08962c 100644
--- a/Marlin/example_configurations/delta/generic/Configuration.h
+++ b/Marlin/example_configurations/delta/generic/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 //===========================================================================
 //============================== Delta Settings =============================
diff --git a/Marlin/example_configurations/delta/kossel_mini/Configuration.h b/Marlin/example_configurations/delta/kossel_mini/Configuration.h
index a39855417c..a6d187cdf1 100644
--- a/Marlin/example_configurations/delta/kossel_mini/Configuration.h
+++ b/Marlin/example_configurations/delta/kossel_mini/Configuration.h
@@ -408,9 +408,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 //===========================================================================
 //============================== Delta Settings =============================
diff --git a/Marlin/example_configurations/delta/kossel_pro/Configuration.h b/Marlin/example_configurations/delta/kossel_pro/Configuration.h
index e66863fba0..ee5cbd1e21 100644
--- a/Marlin/example_configurations/delta/kossel_pro/Configuration.h
+++ b/Marlin/example_configurations/delta/kossel_pro/Configuration.h
@@ -395,9 +395,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 //===========================================================================
 //============================== Delta Settings =============================
diff --git a/Marlin/example_configurations/delta/kossel_xl/Configuration.h b/Marlin/example_configurations/delta/kossel_xl/Configuration.h
index 076a085156..619cab9311 100644
--- a/Marlin/example_configurations/delta/kossel_xl/Configuration.h
+++ b/Marlin/example_configurations/delta/kossel_xl/Configuration.h
@@ -406,9 +406,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 //===========================================================================
 //============================== Delta Settings =============================
diff --git a/Marlin/example_configurations/makibox/Configuration.h b/Marlin/example_configurations/makibox/Configuration.h
index 4364fdfa49..d2e402cb7a 100644
--- a/Marlin/example_configurations/makibox/Configuration.h
+++ b/Marlin/example_configurations/makibox/Configuration.h
@@ -411,9 +411,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 //#define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/example_configurations/tvrrug/Round2/Configuration.h b/Marlin/example_configurations/tvrrug/Round2/Configuration.h
index ec57e30348..48e777a754 100644
--- a/Marlin/example_configurations/tvrrug/Round2/Configuration.h
+++ b/Marlin/example_configurations/tvrrug/Round2/Configuration.h
@@ -398,9 +398,13 @@
 // @section machine
 
 // Uncomment one of these options to enable CoreXY, CoreXZ, or CoreYZ kinematics
+// either in the usual order or reversed
 //#define COREXY
 //#define COREXZ
 //#define COREYZ
+//#define COREYX
+//#define COREZX
+//#define COREZY
 
 // Enable this option for Toshiba steppers
 #define CONFIG_STEPPERS_TOSHIBA
diff --git a/Marlin/planner.cpp b/Marlin/planner.cpp
index bb9379733b..9869373586 100644
--- a/Marlin/planner.cpp
+++ b/Marlin/planner.cpp
@@ -712,24 +712,24 @@ void Planner::_buffer_line(const float &a, const float &b, const float &c, const
 
   // Compute direction bit-mask for this block
   uint8_t dm = 0;
-  #if ENABLED(COREXY)
-    if (da < 0) SBI(dm, X_HEAD); // Save the real Extruder (head) direction in X Axis
-    if (db < 0) SBI(dm, Y_HEAD); // ...and Y
+  #if CORE_IS_XY
+    if (da < 0) SBI(dm, X_HEAD);                // Save the real Extruder (head) direction in X Axis
+    if (db < 0) SBI(dm, Y_HEAD);                // ...and Y
     if (dc < 0) SBI(dm, Z_AXIS);
-    if (da + db < 0) SBI(dm, A_AXIS); // Motor A direction
-    if (da - db < 0) SBI(dm, B_AXIS); // Motor B direction
-  #elif ENABLED(COREXZ)
-    if (da < 0) SBI(dm, X_HEAD); // Save the real Extruder (head) direction in X Axis
+    if (da + db < 0) SBI(dm, A_AXIS);           // Motor A direction
+    if (CORESIGN(da - db) < 0) SBI(dm, B_AXIS); // Motor B direction
+  #elif CORE_IS_XZ
+    if (da < 0) SBI(dm, X_HEAD);                // Save the real Extruder (head) direction in X Axis
     if (db < 0) SBI(dm, Y_AXIS);
-    if (dc < 0) SBI(dm, Z_HEAD); // ...and Z
-    if (da + dc < 0) SBI(dm, A_AXIS); // Motor A direction
-    if (da - dc < 0) SBI(dm, C_AXIS); // Motor C direction
-  #elif ENABLED(COREYZ)
+    if (dc < 0) SBI(dm, Z_HEAD);                // ...and Z
+    if (da + dc < 0) SBI(dm, A_AXIS);           // Motor A direction
+    if (CORESIGN(da - dc) < 0) SBI(dm, C_AXIS); // Motor C direction
+  #elif CORE_IS_YZ
     if (da < 0) SBI(dm, X_AXIS);
-    if (db < 0) SBI(dm, Y_HEAD); // Save the real Extruder (head) direction in Y Axis
-    if (dc < 0) SBI(dm, Z_HEAD); // ...and Z
-    if (db + dc < 0) SBI(dm, B_AXIS); // Motor B direction
-    if (db - dc < 0) SBI(dm, C_AXIS); // Motor C direction
+    if (db < 0) SBI(dm, Y_HEAD);                // Save the real Extruder (head) direction in Y Axis
+    if (dc < 0) SBI(dm, Z_HEAD);                // ...and Z
+    if (db + dc < 0) SBI(dm, B_AXIS);           // Motor B direction
+    if (CORESIGN(db - dc) < 0) SBI(dm, C_AXIS); // Motor C direction
   #else
     if (da < 0) SBI(dm, X_AXIS);
     if (db < 0) SBI(dm, Y_AXIS);
@@ -757,19 +757,16 @@ void Planner::_buffer_line(const float &a, const float &b, const float &c, const
   block->direction_bits = dm;
 
   // Number of steps for each axis
-  #if ENABLED(COREXY)
-    // corexy planning
-    // these equations follow the form of the dA and dB equations on http://www.corexy.com/theory.html
+  // See http://www.corexy.com/theory.html
+  #if CORE_IS_XY
     block->steps[A_AXIS] = labs(da + db);
     block->steps[B_AXIS] = labs(da - db);
     block->steps[Z_AXIS] = labs(dc);
-  #elif ENABLED(COREXZ)
-    // corexz planning
+  #elif CORE_IS_XZ
     block->steps[A_AXIS] = labs(da + dc);
     block->steps[Y_AXIS] = labs(db);
     block->steps[C_AXIS] = labs(da - dc);
-  #elif ENABLED(COREYZ)
-    // coreyz planning
+  #elif CORE_IS_YZ
     block->steps[X_AXIS] = labs(da);
     block->steps[B_AXIS] = labs(db + dc);
     block->steps[C_AXIS] = labs(db - dc);
@@ -804,7 +801,7 @@ void Planner::_buffer_line(const float &a, const float &b, const float &c, const
   block->active_extruder = extruder;
 
   //enable active axes
-  #if ENABLED(COREXY)
+  #if CORE_IS_XY
     if (block->steps[A_AXIS] || block->steps[B_AXIS]) {
       enable_x();
       enable_y();
@@ -812,13 +809,13 @@ void Planner::_buffer_line(const float &a, const float &b, const float &c, const
     #if DISABLED(Z_LATE_ENABLE)
       if (block->steps[Z_AXIS]) enable_z();
     #endif
-  #elif ENABLED(COREXZ)
+  #elif CORE_IS_XZ
     if (block->steps[A_AXIS] || block->steps[C_AXIS]) {
       enable_x();
       enable_z();
     }
     if (block->steps[Y_AXIS]) enable_y();
-  #elif ENABLED(COREYZ)
+  #elif CORE_IS_YZ
     if (block->steps[B_AXIS] || block->steps[C_AXIS]) {
       enable_y();
       enable_z();
@@ -915,26 +912,26 @@ void Planner::_buffer_line(const float &a, const float &b, const float &c, const
    * So we need to create other 2 "AXIS", named X_HEAD and Y_HEAD, meaning the real displacement of the Head.
    * Having the real displacement of the head, we can calculate the total movement length and apply the desired speed.
    */
-  #if ENABLED(COREXY) || ENABLED(COREXZ) || ENABLED(COREYZ)
+  #if IS_CORE
     float delta_mm[7];
-    #if ENABLED(COREXY)
+    #if CORE_IS_XY
       delta_mm[X_HEAD] = da * steps_to_mm[A_AXIS];
       delta_mm[Y_HEAD] = db * steps_to_mm[B_AXIS];
       delta_mm[Z_AXIS] = dc * steps_to_mm[Z_AXIS];
       delta_mm[A_AXIS] = (da + db) * steps_to_mm[A_AXIS];
-      delta_mm[B_AXIS] = (da - db) * steps_to_mm[B_AXIS];
-    #elif ENABLED(COREXZ)
+      delta_mm[B_AXIS] = CORESIGN(da - db) * steps_to_mm[B_AXIS];
+    #elif CORE_IS_XZ
       delta_mm[X_HEAD] = da * steps_to_mm[A_AXIS];
       delta_mm[Y_AXIS] = db * steps_to_mm[Y_AXIS];
       delta_mm[Z_HEAD] = dc * steps_to_mm[C_AXIS];
       delta_mm[A_AXIS] = (da + dc) * steps_to_mm[A_AXIS];
-      delta_mm[C_AXIS] = (da - dc) * steps_to_mm[C_AXIS];
-    #elif ENABLED(COREYZ)
+      delta_mm[C_AXIS] = CORESIGN(da - dc) * steps_to_mm[C_AXIS];
+    #elif CORE_IS_YZ
       delta_mm[X_AXIS] = da * steps_to_mm[X_AXIS];
       delta_mm[Y_HEAD] = db * steps_to_mm[B_AXIS];
       delta_mm[Z_HEAD] = dc * steps_to_mm[C_AXIS];
       delta_mm[B_AXIS] = (db + dc) * steps_to_mm[B_AXIS];
-      delta_mm[C_AXIS] = (db - dc) * steps_to_mm[C_AXIS];
+      delta_mm[C_AXIS] = CORESIGN(db - dc) * steps_to_mm[C_AXIS];
     #endif
   #else
     float delta_mm[4];
@@ -949,11 +946,11 @@ void Planner::_buffer_line(const float &a, const float &b, const float &c, const
   }
   else {
     block->millimeters = sqrt(
-      #if ENABLED(COREXY)
+      #if CORE_IS_XY
         sq(delta_mm[X_HEAD]) + sq(delta_mm[Y_HEAD]) + sq(delta_mm[Z_AXIS])
-      #elif ENABLED(COREXZ)
+      #elif CORE_IS_XZ
         sq(delta_mm[X_HEAD]) + sq(delta_mm[Y_AXIS]) + sq(delta_mm[Z_HEAD])
-      #elif ENABLED(COREYZ)
+      #elif CORE_IS_YZ
         sq(delta_mm[X_AXIS]) + sq(delta_mm[Y_HEAD]) + sq(delta_mm[Z_HEAD])
       #else
         sq(delta_mm[X_AXIS]) + sq(delta_mm[Y_AXIS]) + sq(delta_mm[Z_AXIS])
diff --git a/Marlin/stepper.cpp b/Marlin/stepper.cpp
index 2c6ba5255f..0be61e6465 100644
--- a/Marlin/stepper.cpp
+++ b/Marlin/stepper.cpp
@@ -991,22 +991,22 @@ void Stepper::set_position(const long &a, const long &b, const long &c, const lo
 
   CRITICAL_SECTION_START;
 
-  #if ENABLED(COREXY)
+  #if CORE_IS_XY
     // corexy positioning
     // these equations follow the form of the dA and dB equations on http://www.corexy.com/theory.html
     count_position[A_AXIS] = a + b;
-    count_position[B_AXIS] = a - b;
+    count_position[B_AXIS] = CORESIGN(a - b);
     count_position[Z_AXIS] = c;
-  #elif ENABLED(COREXZ)
+  #elif CORE_IS_XZ
     // corexz planning
     count_position[A_AXIS] = a + c;
     count_position[Y_AXIS] = b;
-    count_position[C_AXIS] = a - c;
-  #elif ENABLED(COREYZ)
+    count_position[C_AXIS] = CORESIGN(a - c);
+  #elif CORE_IS_YZ
     // coreyz planning
     count_position[X_AXIS] = a;
     count_position[B_AXIS] = b + c;
-    count_position[C_AXIS] = b - c;
+    count_position[C_AXIS] = CORESIGN(b - c);
   #else
     // default non-h-bot planning
     count_position[X_AXIS] = a;
@@ -1046,16 +1046,17 @@ long Stepper::position(AxisEnum axis) {
  */
 float Stepper::get_axis_position_mm(AxisEnum axis) {
   float axis_steps;
-  #if ENABLED(COREXY) || ENABLED(COREXZ) || ENABLED(COREYZ)
+  #if IS_CORE
     // Requesting one of the "core" axes?
     if (axis == CORE_AXIS_1 || axis == CORE_AXIS_2) {
       CRITICAL_SECTION_START;
-      long pos1 = count_position[CORE_AXIS_1],
-           pos2 = count_position[CORE_AXIS_2];
-      CRITICAL_SECTION_END;
       // ((a1+a2)+(a1-a2))/2 -> (a1+a2+a1-a2)/2 -> (a1+a1)/2 -> a1
       // ((a1+a2)-(a1-a2))/2 -> (a1+a2-a1+a2)/2 -> (a2+a2)/2 -> a2
-      axis_steps = (pos1 + ((axis == CORE_AXIS_1) ? pos2 : -pos2)) * 0.5f;
+      axis_steps = 0.5f * (
+        axis == CORE_AXIS_2 ? CORESIGN(count_position[CORE_AXIS_1] - count_position[CORE_AXIS_2])
+                            : count_position[CORE_AXIS_1] + count_position[CORE_AXIS_2]
+      );
+      CRITICAL_SECTION_END;
     }
     else
       axis_steps = position(axis);
@@ -1083,14 +1084,12 @@ void Stepper::quick_stop() {
 
 void Stepper::endstop_triggered(AxisEnum axis) {
 
-  #if ENABLED(COREXY) || ENABLED(COREXZ) || ENABLED(COREYZ)
+  #if IS_CORE
 
-    float axis_pos = count_position[axis];
-    if (axis == CORE_AXIS_1)
-      axis_pos = (axis_pos + count_position[CORE_AXIS_2]) * 0.5;
-    else if (axis == CORE_AXIS_2)
-      axis_pos = (count_position[CORE_AXIS_1] - axis_pos) * 0.5;
-    endstops_trigsteps[axis] = axis_pos;
+    endstops_trigsteps[axis] = 0.5f * (
+      axis == CORE_AXIS_2 ? CORESIGN(count_position[CORE_AXIS_1] - count_position[CORE_AXIS_2])
+                          : count_position[CORE_AXIS_1] + count_position[CORE_AXIS_2]
+    );
 
   #else // !COREXY && !COREXZ && !COREYZ
 
@@ -1108,21 +1107,21 @@ void Stepper::report_positions() {
        zpos = count_position[Z_AXIS];
   CRITICAL_SECTION_END;
 
-  #if ENABLED(COREXY) || ENABLED(COREXZ) || IS_SCARA
+  #if CORE_IS_XY || CORE_IS_XZ || IS_SCARA
     SERIAL_PROTOCOLPGM(MSG_COUNT_A);
   #else
     SERIAL_PROTOCOLPGM(MSG_COUNT_X);
   #endif
   SERIAL_PROTOCOL(xpos);
 
-  #if ENABLED(COREXY) || ENABLED(COREYZ) || IS_SCARA
+  #if CORE_IS_XY || CORE_IS_YZ || IS_SCARA
     SERIAL_PROTOCOLPGM(" B:");
   #else
     SERIAL_PROTOCOLPGM(" Y:");
   #endif
   SERIAL_PROTOCOL(ypos);
 
-  #if ENABLED(COREXZ) || ENABLED(COREYZ)
+  #if CORE_IS_XZ || CORE_IS_YZ
     SERIAL_PROTOCOLPGM(" C:");
   #else
     SERIAL_PROTOCOLPGM(" Z:");
diff --git a/Marlin/temperature.h b/Marlin/temperature.h
index 37d47fe5b7..a6b9874c6a 100644
--- a/Marlin/temperature.h
+++ b/Marlin/temperature.h
@@ -385,7 +385,7 @@ class Temperature {
     #if ENABLED(BABYSTEPPING)
 
       static void babystep_axis(const AxisEnum axis, const int distance) {
-        #if ENABLED(COREXY) || ENABLED(COREXZ) || ENABLED(COREYZ)
+        #if IS_CORE
           #if ENABLED(BABYSTEP_XY)
             switch (axis) {
               case CORE_AXIS_1: // X on CoreXY and CoreXZ, Y on CoreYZ
@@ -393,17 +393,17 @@ class Temperature {
                 babystepsTodo[CORE_AXIS_2] += distance * 2;
                 break;
               case CORE_AXIS_2: // Y on CoreXY, Z on CoreXZ and CoreYZ
-                babystepsTodo[CORE_AXIS_1] += distance * 2;
-                babystepsTodo[CORE_AXIS_2] -= distance * 2;
+                babystepsTodo[CORE_AXIS_1] += CORESIGN(distance * 2);
+                babystepsTodo[CORE_AXIS_2] -= CORESIGN(distance * 2);
                 break;
               case NORMAL_AXIS: // Z on CoreXY, Y on CoreXZ, X on CoreYZ
                 babystepsTodo[NORMAL_AXIS] += distance;
                 break;
             }
-          #elif ENABLED(COREXZ) || ENABLED(COREYZ)
+          #elif CORE_IS_XZ || CORE_IS_YZ
             // Only Z stepping needs to be handled here
-            babystepsTodo[CORE_AXIS_1] += distance * 2;
-            babystepsTodo[CORE_AXIS_2] -= distance * 2;
+            babystepsTodo[CORE_AXIS_1] += CORESIGN(distance * 2);
+            babystepsTodo[CORE_AXIS_2] -= CORESIGN(distance * 2);
           #else
             babystepsTodo[Z_AXIS] += distance;
           #endif