diff --git a/Lib/enum.py b/Lib/enum.py
index bc24f2ae2df..5e0088ee89f 100644
--- a/Lib/enum.py
+++ b/Lib/enum.py
@@ -482,14 +482,25 @@ class EnumMeta(type):
             return object, Enum
 
         def _find_data_type(bases):
+            data_types = []
             for chain in bases:
+                candidate = None
                 for base in chain.__mro__:
                     if base is object:
                         continue
                     elif '__new__' in base.__dict__:
                         if issubclass(base, Enum):
                             continue
-                        return base
+                        data_types.append(candidate or base)
+                        break
+                    elif not issubclass(base, Enum):
+                        candidate = base
+            if len(data_types) > 1:
+                raise TypeError('too many data types: %r' % data_types)
+            elif data_types:
+                return data_types[0]
+            else:
+                return None
 
         # ensure final parent class is an Enum derivative, find any concrete
         # data type, and check that Enum has no members
diff --git a/Lib/test/test_enum.py b/Lib/test/test_enum.py
index 138f572906a..a909c108833 100644
--- a/Lib/test/test_enum.py
+++ b/Lib/test/test_enum.py
@@ -560,6 +560,49 @@ class TestEnum(unittest.TestCase):
         self.assertFormatIsValue('{:>20}', Directional.WEST)
         self.assertFormatIsValue('{:<20}', Directional.WEST)
 
+    def test_enum_str_override(self):
+        class MyStrEnum(Enum):
+            def __str__(self):
+                return 'MyStr'
+        class MyMethodEnum(Enum):
+            def hello(self):
+                return 'Hello!  My name is %s' % self.name
+        class Test1Enum(MyMethodEnum, int, MyStrEnum):
+            One = 1
+            Two = 2
+        self.assertEqual(str(Test1Enum.One), 'MyStr')
+        #
+        class Test2Enum(MyStrEnum, MyMethodEnum):
+            One = 1
+            Two = 2
+        self.assertEqual(str(Test2Enum.One), 'MyStr')
+
+    def test_inherited_data_type(self):
+        class HexInt(int):
+            def __repr__(self):
+                return hex(self)
+        class MyEnum(HexInt, enum.Enum):
+            A = 1
+            B = 2
+            C = 3
+        self.assertEqual(repr(MyEnum.A), '<MyEnum.A: 0x1>')
+
+    def test_too_many_data_types(self):
+        with self.assertRaisesRegex(TypeError, 'too many data types'):
+            class Huh(str, int, Enum):
+                One = 1
+
+        class MyStr(str):
+            def hello(self):
+                return 'hello, %s' % self
+        class MyInt(int):
+            def repr(self):
+                return hex(self)
+        with self.assertRaisesRegex(TypeError, 'too many data types'):
+            class Huh(MyStr, MyInt, Enum):
+                One = 1
+
+
     def test_hash(self):
         Season = self.Season
         dates = {}
diff --git a/Misc/NEWS.d/next/Library/2020-09-15-14-56-13.bpo-39587.69xzuh.rst b/Misc/NEWS.d/next/Library/2020-09-15-14-56-13.bpo-39587.69xzuh.rst
new file mode 100644
index 00000000000..e2f2b64867b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-09-15-14-56-13.bpo-39587.69xzuh.rst
@@ -0,0 +1 @@
+use the correct mix-in data type when constructing Enums