diff --git a/django/db/models/sql/query.py b/django/db/models/sql/query.py
index 6c728d17bf..be08c55c7c 100644
--- a/django/db/models/sql/query.py
+++ b/django/db/models/sql/query.py
@@ -631,6 +631,10 @@ class Query(BaseExpression):
         joinpromoter.add_votes(rhs_votes)
         joinpromoter.update_join_types(self)
 
+        # Combine subqueries aliases to ensure aliases relabelling properly
+        # handle subqueries when combining where and select clauses.
+        self.subq_aliases |= rhs.subq_aliases
+
         # Now relabel a copy of the rhs where-clause and add it to the current
         # one.
         w = rhs.where.clone()
diff --git a/docs/releases/3.2.1.txt b/docs/releases/3.2.1.txt
index 4aece451e1..07d449ae8d 100644
--- a/docs/releases/3.2.1.txt
+++ b/docs/releases/3.2.1.txt
@@ -51,3 +51,8 @@ Bugfixes
 * Fixed a bug in Django 3.2 where a system check would crash on the
   :setting:`STATICFILES_DIRS` setting with a list of 2-tuples of
   ``(prefix, path)`` (:ticket:`32665`).
+
+* Fixed a long standing bug involving queryset bitwise combination when used
+  with subqueries that began manifesting in Django 3.2, due to a separate fix
+  using ``Exists`` to ``exclude()`` multi-valued relationships
+  (:ticket:`32650`).
diff --git a/tests/queries/tests.py b/tests/queries/tests.py
index b9b0a72686..a7176240a0 100644
--- a/tests/queries/tests.py
+++ b/tests/queries/tests.py
@@ -2063,36 +2063,50 @@ class SubqueryTests(TestCase):
         )
 
 
-@skipUnlessDBFeature('allow_sliced_subqueries_with_in')
 class QuerySetBitwiseOperationTests(TestCase):
     @classmethod
     def setUpTestData(cls):
-        school = School.objects.create()
-        cls.room_1 = Classroom.objects.create(school=school, has_blackboard=False, name='Room 1')
-        cls.room_2 = Classroom.objects.create(school=school, has_blackboard=True, name='Room 2')
-        cls.room_3 = Classroom.objects.create(school=school, has_blackboard=True, name='Room 3')
-        cls.room_4 = Classroom.objects.create(school=school, has_blackboard=False, name='Room 4')
+        cls.school = School.objects.create()
+        cls.room_1 = Classroom.objects.create(school=cls.school, has_blackboard=False, name='Room 1')
+        cls.room_2 = Classroom.objects.create(school=cls.school, has_blackboard=True, name='Room 2')
+        cls.room_3 = Classroom.objects.create(school=cls.school, has_blackboard=True, name='Room 3')
+        cls.room_4 = Classroom.objects.create(school=cls.school, has_blackboard=False, name='Room 4')
 
+    @skipUnlessDBFeature('allow_sliced_subqueries_with_in')
     def test_or_with_rhs_slice(self):
         qs1 = Classroom.objects.filter(has_blackboard=True)
         qs2 = Classroom.objects.filter(has_blackboard=False)[:1]
         self.assertCountEqual(qs1 | qs2, [self.room_1, self.room_2, self.room_3])
 
+    @skipUnlessDBFeature('allow_sliced_subqueries_with_in')
     def test_or_with_lhs_slice(self):
         qs1 = Classroom.objects.filter(has_blackboard=True)[:1]
         qs2 = Classroom.objects.filter(has_blackboard=False)
         self.assertCountEqual(qs1 | qs2, [self.room_1, self.room_2, self.room_4])
 
+    @skipUnlessDBFeature('allow_sliced_subqueries_with_in')
     def test_or_with_both_slice(self):
         qs1 = Classroom.objects.filter(has_blackboard=False)[:1]
         qs2 = Classroom.objects.filter(has_blackboard=True)[:1]
         self.assertCountEqual(qs1 | qs2, [self.room_1, self.room_2])
 
+    @skipUnlessDBFeature('allow_sliced_subqueries_with_in')
     def test_or_with_both_slice_and_ordering(self):
         qs1 = Classroom.objects.filter(has_blackboard=False).order_by('-pk')[:1]
         qs2 = Classroom.objects.filter(has_blackboard=True).order_by('-name')[:1]
         self.assertCountEqual(qs1 | qs2, [self.room_3, self.room_4])
 
+    def test_subquery_aliases(self):
+        combined = School.objects.filter(pk__isnull=False) & School.objects.filter(
+            Exists(Classroom.objects.filter(
+                has_blackboard=True,
+                school=OuterRef('pk'),
+            )),
+        )
+        self.assertSequenceEqual(combined, [self.school])
+        nested_combined = School.objects.filter(pk__in=combined.values('pk'))
+        self.assertSequenceEqual(nested_combined, [self.school])
+
 
 class CloneTests(TestCase):
 
@@ -2790,6 +2804,21 @@ class ExcludeTests(TestCase):
             )
         self.assertIn('exists', captured_queries[0]['sql'].lower())
 
+    def test_exclude_subquery(self):
+        subquery = JobResponsibilities.objects.filter(
+            responsibility__description='bar',
+        ) | JobResponsibilities.objects.exclude(
+            job__responsibilities__description='foo',
+        )
+        self.assertSequenceEqual(
+            Job.objects.annotate(
+                responsibility=subquery.filter(
+                    job=OuterRef('name'),
+                ).values('id')[:1]
+            ),
+            [self.j1, self.j2],
+        )
+
 
 class ExcludeTest17600(TestCase):
     """