diff --git a/Lib/test/test_cppext/__init__.py b/Lib/test/test_cppext/__init__.py
index 2f54b3ccb35cc4..9013503995bdce 100644
--- a/Lib/test/test_cppext/__init__.py
+++ b/Lib/test/test_cppext/__init__.py
@@ -25,25 +25,11 @@
 @support.requires_subprocess()
 @support.requires_resource('cpu')
 class BaseTests:
+    TEST_INTERNAL_C_API = False
+
     def test_build(self):
         self.check_build('_testcppext')
 
-    def test_build_cpp03(self):
-        # In public docs, we say C API is compatible with C++11. However,
-        # in practice we do maintain C++03 compatibility in public headers.
-        # Please ask the C API WG before adding a new C++11-only feature.
-        self.check_build('_testcpp03ext', std='c++03')
-
-    @unittest.skipIf(support.MS_WINDOWS, "MSVC doesn't support /std:c++11")
-    def test_build_cpp11(self):
-        self.check_build('_testcpp11ext', std='c++11')
-
-    # Only test C++14 on MSVC.
-    # On s390x RHEL7, GCC 4.8.5 doesn't support C++14.
-    @unittest.skipIf(not support.MS_WINDOWS, "need Windows")
-    def test_build_cpp14(self):
-        self.check_build('_testcpp14ext', std='c++14')
-
     def check_build(self, extension_name, std=None, limited=False):
         venv_dir = 'env'
         with support.setup_venv_with_pip_setuptools(venv_dir) as python_exe:
@@ -63,6 +49,7 @@ def run_cmd(operation, cmd):
             if limited:
                 env['CPYTHON_TEST_LIMITED'] = '1'
             env['CPYTHON_TEST_EXT_NAME'] = extension_name
+            env['TEST_INTERNAL_C_API'] = str(int(self.TEST_INTERNAL_C_API))
             if support.verbose:
                 print('Run:', ' '.join(map(shlex.quote, cmd)))
                 subprocess.run(cmd, check=True, env=env)
@@ -112,6 +99,22 @@ def test_build_limited_cpp03(self):
     def test_build_limited(self):
         self.check_build('_testcppext_limited', limited=True)
 
+    def test_build_cpp03(self):
+        # In public docs, we say C API is compatible with C++11. However,
+        # in practice we do maintain C++03 compatibility in public headers.
+        # Please ask the C API WG before adding a new C++11-only feature.
+        self.check_build('_testcpp03ext', std='c++03')
+
+    @unittest.skipIf(support.MS_WINDOWS, "MSVC doesn't support /std:c++11")
+    def test_build_cpp11(self):
+        self.check_build('_testcpp11ext', std='c++11')
+
+    # Only test C++14 on MSVC.
+    # On s390x RHEL7, GCC 4.8.5 doesn't support C++14.
+    @unittest.skipIf(not support.MS_WINDOWS, "need Windows")
+    def test_build_cpp14(self):
+        self.check_build('_testcpp14ext', std='c++14')
+
 
 class TestInteralCAPI(BaseTests, unittest.TestCase):
     TEST_INTERNAL_C_API = True
diff --git a/Lib/test/test_cppext/extension.cpp b/Lib/test/test_cppext/extension.cpp
index f95655eccded61..038f67bbbe3f74 100644
--- a/Lib/test/test_cppext/extension.cpp
+++ b/Lib/test/test_cppext/extension.cpp
@@ -7,15 +7,22 @@
 #undef NDEBUG
 
 #ifdef TEST_INTERNAL_C_API
-#  define Py_BUILD_CORE 1
+#  define Py_BUILD_CORE_MODULE 1
 #endif
 
 #include "Python.h"
 
 #ifdef TEST_INTERNAL_C_API
    // gh-135906: Check for compiler warnings in the internal C API
-#  include "internal/pycore_backoff.h"
 #  include "internal/pycore_frame.h"
+   // mimalloc emits many compiler warnings when Python is built in debug
+   // mode (when MI_DEBUG is not zero)
+   // mimalloc emits compiler warnings when Python is built on Windows
+   // in free-threaded mode.
+#  if !defined(Py_DEBUG) && !(defined(MS_WINDOWS) && defined(Py_GIL_DISABLED))
+#    include "internal/pycore_backoff.h"
+#    include "internal/pycore_cell.h"
+#  endif
 #endif
 
 #ifndef MODULE_NAME