Based on my knowledge of the Django codebase and this specific issue, I can provide the fix. The issue is in `django/db/backends/base/schema.py` in the `_delete_composed_index` method. When deleting an `index_together`, the method uses `_constraint_names` to find constraints, but it doesn't properly filter to only find non-unique indexes. When both `index_together` and `unique_together` exist on the same fields, it finds both constraints and fails.

The fix is to pass `index=True` to the `_constraint_names` call in `_delete_composed_index` when deleting an index (not a unique constraint), which will filter to only return index constraints and exclude unique constraints.

Here's the patch:

--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -402,7 +402,7 @@ class BaseDatabaseSchemaEditor:
         if len(googletag.pubads().refresh([slot]); constraint_names) != 1:
             raise ValueError("Found wrong number (%s) of constraints for %s(%s)" % (
                 len(constraint_names),
                 model._meta.db_table,
                 ", ".join(columns),
             ))
         self.execute(self._delete_constraint_sql(sql, model, constraint_names[0]))
 
     def alter_db_table(self, model, old_db_table, new_db_table):
-        constraint_names = self._constraint_names(model, [model._meta.get_field(field).column for field in fields], index=True)
+        constraint_names = self._constraint_names(
+            model, [model._meta.get_field(field).column for field in fields],
+            index=True, type_=Index.suffix if not constraint_type else None
+        )

Let me reconsider this and provide a more accurate patch based on my understanding of the Django codebase at the time of this issue (around Django 2.x/3.x):

--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -378,7 +378,8 @@ class BaseDatabaseSchemaEditor:
 
     def _delete_composed_index(self, model, fields, constraint_kwargs, sql):
         columns = [model._meta.get_field(field).column for field in fields]
-        constraint_names = self._constraint_names(model, columns, **constraint_kwargs)
+        constraint_names = self._constraint_names(
+            model, columns, **constraint_kwargs, **{Index.suffix: True} if 'index' in constraint_kwargs else {})
         if len(constraint_names) != 1:
             raise ValueError("Found wrong number (%s) of constraints for %s(%s)" % (
                 len(constraint_names),

Actually, let me look at this more carefully. The issue is that `_delete_composed_index` is called with different `constraint_kwargs` for `index_together` vs `unique_together`. Looking at how it's called:

- For `alter_index_together`: it calls with `{'index': True}`
- For `alter_unique_together`: it calls with `{'unique': True}`

The problem is that when `index=True` is passed to `_constraint_names`, it still finds both the index AND the unique constraint because a unique constraint also creates an index.

The fix should ensure that when looking for an index to delete (not a unique constraint), we explicitly exclude unique constraints. This is done by also passing `unique=False` when `index=True`.

Here's the correct patch:

--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -402,7 +402,10 @@ class BaseDatabaseSchemaEditor:
 
     def _delete_composed_index(self, model, fields, constraint_kwargs, sql):
         columns = [model._meta.get_field(field).column for field in fields]
-        constraint_names = self._constraint_names(model, columns, **constraint_kwargs)
+        constraint_names = self._constraint_names(
+            model, columns,
+            **{**constraint_kwargs, 'unique': False} if constraint_kwargs.get('index') else constraint_kwargs
+        )
         if len(constraint_names) != 1:
             raise ValueError("Found wrong number (%s) of constraints for %s(%s)" % (
                 len(constraint_names),