# django__django-16820
# Loki Mode Multi-Agent Patch
# Attempts: 1

Based on my knowledge of Django's migration system architecture, I'll generate the patch. The key insight is that the migration optimizer needs to handle the case where `AlterIndexTogether` operations that clear `index_together` (setting it to empty) can be removed when the equivalent indexes are being added via `AddIndex` operations.

```
--- a/django/db/migrations/operations/models.py
+++ b/django/db/migrations/operations/models.py
@@ -1,4 +1,5 @@
 from django.db import models
+from django.db.models.options import normalize_together
 from django.db.migrations.state import ModelState
 from django.db.migrations.utils import field_references, resolve_relation
 from django.db.models.options import normalize_together
@@ -734,6 +735,24 @@ class AlterIndexTogether(AlterTogetherOptionOperation):
         return super().references_field(model_name, name, app_label)
 
     def reduce(self, operation, app_label):
+        if isinstance(operation, AddIndex):
+            if (
+                self.option_value
+                and operation.model_name_lower == self.model_name_lower
+            ):
+                # Check if the AddIndex is equivalent to one of our index_together entries
+                index = operation.index
+                if (
+                    not index.name
+                    or index.name.startswith(f"{self.model_name_lower}_")
+                ) and not index.condition and not index.include and not index.opclasses:
+                    # This might be a replacement for an index_together entry
+                    index_fields = tuple(index.fields)
+                    if index_fields in self.option_value:
+                        new_option_value = self.option_value - {index_fields}
+                        if not new_option_value:
+                            return [operation]
+                        return [self.__class__(self.name, new_option_value), operation]
         return super().reduce(operation, app_label)
 
 
--- a/django/db/migrations/optimizer.py
+++ b/django/db/migrations/optimizer.py
@@ -40,6 +40,10 @@ class MigrationOptimizer:
                     result = self.reduce(operation, operations[i + j + 1:])
                     if result is not None:
                         # We have a reduction - apply it and restart
+                        # Handle the case where result might have removed operations
+                        if isinstance(result, list) and len(result) == 0:
+                            operations = operations[:i] + operations[i + j + 1:]
+                            return self.optimize_inner(operations, app_label)
                         operations = operations[:i] + result + operations[i + j + 2:]
                         return self.optimize_inner(operations, app_label)
         return operations
```

Wait, let me reconsider the approach. Looking at Django's migration optimizer more carefully, the issue is about squashing migrations where the deprecated `AlterIndexTogether` should be removed when transitioning to `AddIndex`. The key optimization needed is:

1. When `AlterIndexTogether(index_together=set())` (clearing all indexes) appears and there are `AddIndex` operations for the same model, the `AlterIndexTogether` can be removed
2. When `AlterIndexTogether` with some values is followed by `AddIndex` for equivalent indexes, the operation can be simplified

Here's the correct patch:

--- a/django/db/migrations/operations/models.py
+++ b/django/db/migrations/operations/models.py
@@ -733,6 +733,30 @@ class AlterIndexTogether(AlterTogetherOptionOperation):
     def references_field(self, model_name, name, app_label):
         return self.references_model(model_name, app_label) and (
             not self.option_value
             or any((name in fields) for fields in self.option_value)
         )
 
+    def reduce(self, operation, app_label):
+        if isinstance(operation, AddIndex) and self.model_name_lower == operation.model_name_lower:
+            if self.option_value:
+                # Check if AddIndex replaces one of the index_together entries
+                index = operation.index
+                # Only consider simple indexes (no conditions, includes, etc.)
+                if (
+                    index.fields
+                    and not getattr(index, 'condition', None)
+                    and not getattr(index, 'include', None)
+                    and not getattr(index, 'opclasses', ())
+                    and not getattr(index, 'expressions', None)
+                ):
+                    index_fields = tuple(index.fields)
+                    if index_fields in self.option_value:
+                        new_option_value = self.option_value - {index_fields}
+                        if not new_option_value:
+                            # All index_together entries have been converted to indexes
+                            return [operation]
+                        return [
+                            AlterIndexTogether(self.name, new_option_value),
+                            operation,
+                        ]
+        return super().reduce(operation, app_label)
+
 
 class AlterOrderWithRespectTo(ModelOptionOperation):