diff --git a/aesara/tensor/rewriting/elemwise.py b/aesara/tensor/rewriting/elemwise.py
index 08449bfc55..1973277da2 100644
--- a/aesara/tensor/rewriting/elemwise.py
+++ b/aesara/tensor/rewriting/elemwise.py
@@ -52,6 +52,14 @@ def print_profile(cls, stream, prof, level=0):
             for n in sorted(ndim.keys()):
                 print(blanc, n, ndim[n], file=stream)
 
+    def candidate_input_idxs(self, node):
+        if isinstance(node.op.scalar_op, aes.Composite) and len(node.outputs) > 1:
+            # TODO: Implement specialized InplaceCompositeOptimizer with logic
+            #  needed to correctly assign inplace for multi-output Composites
+            return []
+        else:
+            return range(len(node.outputs))
+
     def apply(self, fgraph):
         r"""
 
@@ -142,7 +150,7 @@ def apply(self, fgraph):
 
                 baseline = op.inplace_pattern
                 candidate_outputs = [
-                    i for i in range(len(node.outputs)) if i not in baseline
+                    i for i in self.candidate_input_idxs(node) if i not in baseline
                 ]
                 # node inputs that are Constant, already destroyed,
                 # or fgraph protected inputs and fgraph outputs can't be used as
@@ -160,7 +168,7 @@ def apply(self, fgraph):
                 ]
             else:
                 baseline = []
-                candidate_outputs = list(range(len(node.outputs)))
+                candidate_outputs = self.candidate_input_idxs(node)
                 # node inputs that are Constant, already destroyed,
                 # fgraph protected inputs and fgraph outputs can't be used as inplace
                 # target.