prevent unacceptable bases from becoming bases through multiple inheritance (#24806)
diff --git a/Lib/test/test_descr.py b/Lib/test/test_descr.py
index 0ac458f..25f65c5 100644
--- a/Lib/test/test_descr.py
+++ b/Lib/test/test_descr.py
@@ -4065,6 +4065,37 @@
         else:
             assert 0, "best_base calculation found wanting"
 
+    def test_unsubclassable_types(self):
+        with self.assertRaises(TypeError):
+            class X(types.NoneType):
+                pass
+        with self.assertRaises(TypeError):
+            class X(object, types.NoneType):
+                pass
+        with self.assertRaises(TypeError):
+            class X(types.NoneType, object):
+                pass
+        class O(object):
+            pass
+        with self.assertRaises(TypeError):
+            class X(O, types.NoneType):
+                pass
+        with self.assertRaises(TypeError):
+            class X(types.NoneType, O):
+                pass
+
+        class X(object):
+            pass
+        with self.assertRaises(TypeError):
+            X.__bases__ = types.NoneType,
+        with self.assertRaises(TypeError):
+            X.__bases__ = object, types.NoneType
+        with self.assertRaises(TypeError):
+            X.__bases__ = types.NoneType, object
+        with self.assertRaises(TypeError):
+            X.__bases__ = O, types.NoneType
+        with self.assertRaises(TypeError):
+            X.__bases__ = types.NoneType, O
 
     def test_mutable_bases_with_failing_mro(self):
         # Testing mutable bases with failing mro...
diff --git a/Misc/NEWS b/Misc/NEWS
index eb43f1f..60dfbf0 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -10,6 +10,9 @@
 Core and Builtins
 -----------------
 
+- Issue #24806: Prevent builtin types that are not allowed to be subclassed from
+  being subclassed through multiple inheritance.
+
 - Issue #24848: Fixed a number of bugs in UTF-7 decoding of misformed data.
 
 - Issue #25003: os.urandom() doesn't use getentropy() on Solaris because
diff --git a/Objects/typeobject.c b/Objects/typeobject.c
index 9a221b3..d3e5384 100644
--- a/Objects/typeobject.c
+++ b/Objects/typeobject.c
@@ -1724,6 +1724,12 @@
             if (PyType_Ready(base_i) < 0)
                 return NULL;
         }
+        if (!PyType_HasFeature(base_i, Py_TPFLAGS_BASETYPE)) {
+            PyErr_Format(PyExc_TypeError,
+                         "type '%.100s' is not an acceptable base type",
+                         base_i->tp_name);
+            return NULL;
+        }
         candidate = solid_base(base_i);
         if (winner == NULL) {
             winner = candidate;
@@ -2148,13 +2154,6 @@
         Py_DECREF(bases);
         return NULL;
     }
-    if (!PyType_HasFeature(base, Py_TPFLAGS_BASETYPE)) {
-        PyErr_Format(PyExc_TypeError,
-                     "type '%.100s' is not an acceptable base type",
-                     base->tp_name);
-        Py_DECREF(bases);
-        return NULL;
-    }
 
     /* Check for a __slots__ sequence variable in dict, and count it */
     slots = PyDict_GetItemString(dict, "__slots__");