diff --git a/django/db/backends/schema.py b/django/db/backends/schema.py
index d0c4639d7fd..2a62803a731 100644
--- a/django/db/backends/schema.py
+++ b/django/db/backends/schema.py
@@ -483,8 +483,11 @@ class BaseDatabaseSchemaEditor(object):
         new_type = new_db_params['type']
         if old_type is None and new_type is None and (old_field.rel.through and new_field.rel.through and old_field.rel.through._meta.auto_created and new_field.rel.through._meta.auto_created):
             return self._alter_many_to_many(model, old_field, new_field, strict)
+        elif old_type is None and new_type is None and (old_field.rel.through and new_field.rel.through and not old_field.rel.through._meta.auto_created and not new_field.rel.through._meta.auto_created):
+            # Both sides have through models; this is a no-op.
+            return
         elif old_type is None or new_type is None:
-            raise ValueError("Cannot alter field %s into %s - they are not compatible types (probably means only one is an M2M with implicit through model)" % (
+            raise ValueError("Cannot alter field %s into %s - they are not compatible types (you cannot alter to or from M2M fields, or add or remove through= on M2M fields)" % (
                 old_field,
                 new_field,
             ))
diff --git a/django/db/backends/sqlite3/schema.py b/django/db/backends/sqlite3/schema.py
index 005d4b13c86..5b6155be47f 100644
--- a/django/db/backends/sqlite3/schema.py
+++ b/django/db/backends/sqlite3/schema.py
@@ -148,8 +148,11 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
         new_type = new_db_params['type']
         if old_type is None and new_type is None and (old_field.rel.through and new_field.rel.through and old_field.rel.through._meta.auto_created and new_field.rel.through._meta.auto_created):
             return self._alter_many_to_many(model, old_field, new_field, strict)
+        elif old_type is None and new_type is None and (old_field.rel.through and new_field.rel.through and not old_field.rel.through._meta.auto_created and not new_field.rel.through._meta.auto_created):
+            # Both sides have through models; this is a no-op.
+            return
         elif old_type is None or new_type is None:
-            raise ValueError("Cannot alter field %s into %s - they are not compatible types (probably means only one is an M2M with implicit through model)" % (
+            raise ValueError("Cannot alter field %s into %s - they are not compatible types (you cannot alter to or from M2M fields, or add or remove through= on M2M fields)" % (
                 old_field,
                 new_field,
             ))
diff --git a/tests/schema/models.py b/tests/schema/models.py
index f85a3c6362e..f5f59f7416d 100644
--- a/tests/schema/models.py
+++ b/tests/schema/models.py
@@ -24,6 +24,22 @@ class AuthorWithM2M(models.Model):
         apps = new_apps
 
 
+class AuthorWithM2MThrough(models.Model):
+    name = models.CharField(max_length=255)
+    tags = models.ManyToManyField("schema.TagM2MTest", related_name="authors", through="AuthorTag")
+
+    class Meta:
+        apps = new_apps
+
+
+class AuthorTag(models.Model):
+    author = models.ForeignKey("schema.AuthorWithM2MThrough")
+    tag = models.ForeignKey("schema.TagM2MTest")
+
+    class Meta:
+        apps = new_apps
+
+
 class Book(models.Model):
     author = models.ForeignKey(Author)
     title = models.CharField(max_length=100, db_index=True)
diff --git a/tests/schema/tests.py b/tests/schema/tests.py
index 55b2ee5ce39..371eaadecbd 100644
--- a/tests/schema/tests.py
+++ b/tests/schema/tests.py
@@ -9,7 +9,7 @@ from django.db.models.fields.related import ManyToManyField, ForeignKey
 from django.db.transaction import atomic
 from .models import (Author, AuthorWithM2M, Book, BookWithLongName,
     BookWithSlug, BookWithM2M, Tag, TagIndexed, TagM2MTest, TagUniqueRename,
-    UniqueTest, Thing, TagThrough, BookWithM2MThrough)
+    UniqueTest, Thing, TagThrough, BookWithM2MThrough, AuthorTag, AuthorWithM2MThrough)
 
 
 class SchemaTests(TransactionTestCase):
@@ -402,6 +402,30 @@ class SchemaTests(TransactionTestCase):
             # Cleanup model states
             AuthorWithM2M._meta.local_many_to_many.remove(new_field)
 
+    def test_m2m_through_alter(self):
+        """
+        Tests altering M2Ms with explicit through models (should no-op)
+        """
+        # Create the tables
+        with connection.schema_editor() as editor:
+            editor.create_model(AuthorTag)
+            editor.create_model(AuthorWithM2MThrough)
+            editor.create_model(TagM2MTest)
+        # Ensure the m2m table is there
+        self.assertEqual(len(self.column_classes(AuthorTag)), 3)
+        # "Alter" the field's blankness. This should not actually do anything.
+        with connection.schema_editor() as editor:
+            old_field = AuthorWithM2MThrough._meta.get_field_by_name("tags")[0]
+            new_field = ManyToManyField("schema.TagM2MTest", related_name="authors", through="AuthorTag")
+            new_field.contribute_to_class(AuthorWithM2MThrough, "tags")
+            editor.alter_field(
+                Author,
+                old_field,
+                new_field,
+            )
+        # Ensure the m2m table is still there
+        self.assertEqual(len(self.column_classes(AuthorTag)), 3)
+
     def test_m2m_repoint(self):
         """
         Tests repointing M2M fields