diff --git a/pytensor/printing.py b/pytensor/printing.py
index b7b71622e8..5bdac3e7fd 100644
--- a/pytensor/printing.py
+++ b/pytensor/printing.py
@@ -88,6 +88,7 @@ def debugprint(
     | FunctionGraph
     | Sequence[Variable | Apply | Function | FunctionGraph],
     depth: int = -1,
+    inner_depth: int = -1,
     print_type: bool = False,
     print_shape: bool = False,
     file: Literal["str"] | TextIO | None = None,
@@ -123,6 +124,8 @@ def debugprint(
         The object(s) to be printed.
     depth
         Print graph to this depth (``-1`` for unlimited).
+    inner_depth
+        Print inner graph to this depth (``-1`` for unlimited).
     print_type
         If ``True``, print the `Type`\s of each `Variable` in the graph.
     print_shape
@@ -161,6 +164,8 @@ def debugprint(
         Whether to set both `print_destroy_map` and `print_view_map` to ``True``.
     print_fgraph_inputs
         Print the inputs of `FunctionGraph`\s.
+    print_inner_graphs
+        Whether to print the inner graphs of `Op`\s
 
     Returns
     -------
@@ -293,10 +298,14 @@ def debugprint(
     ):
         if hasattr(var.owner, "op"):
             if (
-                isinstance(var.owner.op, HasInnerGraph)
-                or hasattr(var.owner.op, "scalar_op")
-                and isinstance(var.owner.op.scalar_op, HasInnerGraph)
-            ) and var not in inner_graph_vars:
+                (
+                    isinstance(var.owner.op, HasInnerGraph)
+                    or hasattr(var.owner.op, "scalar_op")
+                    and isinstance(var.owner.op.scalar_op, HasInnerGraph)
+                )
+                and inner_depth
+                and var not in inner_graph_vars
+            ):
                 inner_graph_vars.append(var)
             if print_op_info:
                 op_information.update(op_debug_information(var.owner.op, var.owner))
@@ -322,7 +331,7 @@ def debugprint(
             print_view_map=print_view_map,
         )
 
-    if len(inner_graph_vars) > 0:
+    if len(inner_graph_vars) > 0 and inner_depth:
         print("", file=_file)
         prefix = ""
         new_prefix = prefix + " ← "
@@ -374,7 +383,7 @@ def debugprint(
             _debugprint(
                 ig_var,
                 prefix=prefix,
-                depth=depth,
+                depth=inner_depth,
                 done=done,
                 print_type=print_type,
                 print_shape=print_shape,
@@ -397,7 +406,7 @@ def debugprint(
                     _debugprint(
                         inp,
                         prefix=" → ",
-                        depth=depth,
+                        depth=inner_depth,
                         done=done,
                         print_type=print_type,
                         print_shape=print_shape,
@@ -432,7 +441,7 @@ def debugprint(
                 _debugprint(
                     out,
                     prefix=new_prefix,
-                    depth=depth,
+                    depth=inner_depth,
                     done=done,
                     print_type=print_type,
                     print_shape=print_shape,