diff --git a/Include/moduleobject.h b/Include/moduleobject.h
index ea08145381cee62..2f7dc254466c46f 100644
--- a/Include/moduleobject.h
+++ b/Include/moduleobject.h
@@ -79,12 +79,14 @@ struct PyModuleDef_Slot {
 #define _Py_mod_LAST_SLOT 3
 #endif
 
+#endif /* New in 3.5 */
+
 /* for Py_mod_multiple_interpreters: */
+#if !defined(Py_LIMITED_API) || Py_LIMITED_API+0 >= 0x030d0000
 #define Py_MOD_MULTIPLE_INTERPRETERS_NOT_SUPPORTED ((void *)0)
 #define Py_MOD_MULTIPLE_INTERPRETERS_SUPPORTED ((void *)1)
 #define Py_MOD_PER_INTERPRETER_GIL_SUPPORTED ((void *)2)
-
-#endif /* New in 3.5 */
+#endif
 
 struct PyModuleDef {
   PyModuleDef_Base m_base;
diff --git a/Modules/_ctypes/_ctypes_test.c b/Modules/_ctypes/_ctypes_test.c
index 11c7a6b8926214e..5473310ded07343 100644
--- a/Modules/_ctypes/_ctypes_test.c
+++ b/Modules/_ctypes/_ctypes_test.c
@@ -1,8 +1,11 @@
-#define Py_LIMITED_API 0x03060000
+// Need limited C API version 3.13 for Py_MOD_PER_INTERPRETER_GIL_SUPPORTED
+#define Py_LIMITED_API 0x030d0000
 
 #include <Python.h>
 
+#include <stdio.h>                // printf()
 #include <stdlib.h>               // qsort()
+#include <string.h>               // memset()
 #ifdef MS_WIN32
 #  include <windows.h>
 #endif
diff --git a/Modules/errnomodule.c b/Modules/errnomodule.c
index 25cd7e9ae0e122d..e4fd3b47762702f 100644
--- a/Modules/errnomodule.c
+++ b/Modules/errnomodule.c
@@ -1,9 +1,10 @@
 /* Errno module */
 
-// Need PyModuleDef_Slot added to limited C API version 3.5
-#define Py_LIMITED_API 0x03050000
+// Need limited C API version 3.13 for Py_MOD_PER_INTERPRETER_GIL_SUPPORTED
+#define Py_LIMITED_API 0x030d0000
 
 #include "Python.h"
+#include <errno.h>                // EPIPE
 
 /* Windows socket errors (WSA*)  */
 #ifdef MS_WINDOWS
diff --git a/Modules/xxlimited.c b/Modules/xxlimited.c
index 3935c00fc26530a..df6e593b320e522 100644
--- a/Modules/xxlimited.c
+++ b/Modules/xxlimited.c
@@ -62,7 +62,8 @@
           pass
    */
 
-#define Py_LIMITED_API 0x030b0000
+// Need limited C API version 3.13 for Py_MOD_PER_INTERPRETER_GIL_SUPPORTED
+#define Py_LIMITED_API 0x030d0000
 
 #include "Python.h"
 #include <string.h>
diff --git a/Modules/xxlimited_35.c b/Modules/xxlimited_35.c
index 1ff3ef1cb6f296e..361c7e76d77f508 100644
--- a/Modules/xxlimited_35.c
+++ b/Modules/xxlimited_35.c
@@ -293,7 +293,6 @@ xx_modexec(PyObject *m)
 
 static PyModuleDef_Slot xx_slots[] = {
     {Py_mod_exec, xx_modexec},
-    {Py_mod_multiple_interpreters, Py_MOD_PER_INTERPRETER_GIL_SUPPORTED},
     {0, NULL}
 };