diff --git a/django/db/models/fields/related.py b/django/db/models/fields/related.py
index a59dcac68c..9ad440128e 100644
--- a/django/db/models/fields/related.py
+++ b/django/db/models/fields/related.py
@@ -626,9 +626,10 @@ class ForeignObject(RelatedField):
                 if isinstance(field, CompositePrimaryKey):
                     errors.append(
                         checks.Error(
-                            "Field defines a relation to the CompositePrimaryKey of "
-                            f"model {self.remote_field.model._meta.object_name!r} "
-                            "which is not supported.",
+                            "Field defines a relation involving model "
+                            f"{self.remote_field.model._meta.object_name!r} which has "
+                            "a CompositePrimaryKey and such relations are not "
+                            "supported.",
                             obj=self,
                             id="fields.E347",
                         )
@@ -1538,20 +1539,24 @@ class ManyToManyField(RelatedField):
                 to_model_name = to_model
             else:
                 to_model_name = to_model._meta.object_name
-            if (
-                self.remote_field.through_fields is None
-                and not isinstance(to_model, str)
-                and isinstance(to_model._meta.pk, CompositePrimaryKey)
+            if self.remote_field.through_fields is None and not isinstance(
+                to_model, str
             ):
-                errors.append(
-                    checks.Error(
-                        "Field defines a relation to the CompositePrimaryKey of model "
-                        f"{self.remote_field.model._meta.object_name!r} which is not "
-                        "supported.",
-                        obj=self,
-                        id="fields.E347",
+                model_name = None
+                if isinstance(to_model._meta.pk, CompositePrimaryKey):
+                    model_name = self.remote_field.model._meta.object_name
+                elif isinstance(from_model._meta.pk, CompositePrimaryKey):
+                    model_name = from_model_name
+                if model_name:
+                    errors.append(
+                        checks.Error(
+                            f"Field defines a relation involving model {model_name!r} "
+                            "which has a CompositePrimaryKey and such relations are "
+                            "not supported.",
+                            obj=self,
+                            id="fields.E347",
+                        )
                     )
-                )
             relationship_model_name = self.remote_field.through._meta.object_name
             self_referential = from_model == to_model
             # Count foreign keys in intermediate model
diff --git a/docs/ref/checks.txt b/docs/ref/checks.txt
index bb54dbdb98..51f6c282c6 100644
--- a/docs/ref/checks.txt
+++ b/docs/ref/checks.txt
@@ -338,8 +338,8 @@ Related fields
 * **fields.W345**: ``related_name`` has no effect on ``ManyToManyField`` with a
   symmetrical relationship, e.g. to "self".
 * **fields.W346**: ``db_comment`` has no effect on ``ManyToManyField``.
-* **fields.E347**: Field defines a relation to the ``CompositePrimaryKey`` of
-  model ``<model>`` which is not supported.
+* **fields.E347**: Field defines a relation involving model ``<model>`` which
+  has a ``CompositePrimaryKey`` and such relations are not supported.
 * **fields.E348**: Related name ``<related_name>`` for ``<model>.<field name>``
   clashes with the name of a model manager.
 
diff --git a/docs/releases/5.2.5.txt b/docs/releases/5.2.5.txt
index 6791983aad..f782ea9632 100644
--- a/docs/releases/5.2.5.txt
+++ b/docs/releases/5.2.5.txt
@@ -21,3 +21,7 @@ Bugfixes
   (:ticket:`36518`).
 
 * Added compatibility for ``docutils`` 0.22 (:ticket:`36535`).
+
+* Fixed a crash in Django 5.2 when using a ``ManyToManyField`` on a model with
+  a composite primary key, by extending the ``fields.E347`` system check
+  (:ticket:`36530`).
diff --git a/tests/invalid_models_tests/test_relative_fields.py b/tests/invalid_models_tests/test_relative_fields.py
index 82e5a954bd..ed6d39f7c6 100644
--- a/tests/invalid_models_tests/test_relative_fields.py
+++ b/tests/invalid_models_tests/test_relative_fields.py
@@ -454,29 +454,19 @@ class RelativeFieldTests(SimpleTestCase):
                 "Parent", on_delete=models.CASCADE, related_name="child_string_set"
             )
 
+        error = (
+            "Field defines a relation involving model 'Parent' which has a "
+            "CompositePrimaryKey and such relations are not supported."
+        )
         field = Child._meta.get_field("rel_string_parent")
         self.assertEqual(
             field.check(),
-            [
-                Error(
-                    "Field defines a relation to the CompositePrimaryKey of model "
-                    "'Parent' which is not supported.",
-                    obj=field,
-                    id="fields.E347",
-                ),
-            ],
+            [Error(error, obj=field, id="fields.E347")],
         )
         field = Child._meta.get_field("rel_class_parent")
         self.assertEqual(
             field.check(),
-            [
-                Error(
-                    "Field defines a relation to the CompositePrimaryKey of model "
-                    "'Parent' which is not supported.",
-                    obj=field,
-                    id="fields.E347",
-                ),
-            ],
+            [Error(error, obj=field, id="fields.E347")],
         )
 
     def test_many_to_many_to_model_with_composite_primary_key(self):
@@ -493,29 +483,45 @@ class RelativeFieldTests(SimpleTestCase):
                 "Parent", related_name="child_string_set"
             )
 
+        error = (
+            "Field defines a relation involving model 'Parent' which has a "
+            "CompositePrimaryKey and such relations are not supported."
+        )
         field = Child._meta.get_field("rel_string_parent")
         self.assertEqual(
             field.check(from_model=Child),
-            [
-                Error(
-                    "Field defines a relation to the CompositePrimaryKey of model "
-                    "'Parent' which is not supported.",
-                    obj=field,
-                    id="fields.E347",
-                ),
-            ],
+            [Error(error, obj=field, id="fields.E347")],
         )
         field = Child._meta.get_field("rel_class_parent")
         self.assertEqual(
             field.check(from_model=Child),
-            [
-                Error(
-                    "Field defines a relation to the CompositePrimaryKey of model "
-                    "'Parent' which is not supported.",
-                    obj=field,
-                    id="fields.E347",
-                ),
-            ],
+            [Error(error, obj=field, id="fields.E347")],
+        )
+
+    def test_many_to_many_from_model_with_composite_primary_key(self):
+        class Parent(models.Model):
+            name = models.CharField(max_length=20)
+
+            class Meta:
+                app_label = "invalid_models_tests"
+
+        class Child(models.Model):
+            pk = models.CompositePrimaryKey("version", "name")
+            version = models.IntegerField()
+            name = models.CharField(max_length=20)
+            parents = models.ManyToManyField(Parent)
+
+            class Meta:
+                app_label = "invalid_models_tests"
+
+        error = (
+            "Field defines a relation involving model 'Child' which has a "
+            "CompositePrimaryKey and such relations are not supported."
+        )
+        field = Child._meta.get_field("parents")
+        self.assertEqual(
+            field.check(from_model=Child),
+            [Error(error, obj=field, id="fields.E347")],
         )
 
     def test_foreign_key_to_non_unique_field(self):
@@ -1038,8 +1044,8 @@ class RelativeFieldTests(SimpleTestCase):
             field.check(),
             [
                 Error(
-                    "Field defines a relation to the CompositePrimaryKey of model "
-                    "'Parent' which is not supported.",
+                    "Field defines a relation involving model 'Parent' which has a "
+                    "CompositePrimaryKey and such relations are not supported.",
                     obj=field,
                     id="fields.E347",
                 ),
@@ -1060,8 +1066,8 @@ class RelativeFieldTests(SimpleTestCase):
             field.check(),
             [
                 Error(
-                    "Field defines a relation to the CompositePrimaryKey of model "
-                    "'Parent' which is not supported.",
+                    "Field defines a relation involving model 'Parent' which has a "
+                    "CompositePrimaryKey and such relations are not supported.",
                     obj=field,
                     id="fields.E347",
                 ),