diff --git a/tests/v1/engine/test_output_processor.py b/tests/v1/engine/test_output_processor.py
index 9ac42dbc34a4..f8d96caf1a27 100644
--- a/tests/v1/engine/test_output_processor.py
+++ b/tests/v1/engine/test_output_processor.py
@@ -921,3 +921,84 @@ async def test_request_output_collector():
     # Cumulative logprobs should be the last one.
     cumulative_logprob_expected = 1.0 * num_to_put
     assert output.outputs[0].cumulative_logprob == cumulative_logprob_expected
+
+
+@pytest.mark.asyncio
+async def test_cumulative_output_collector_n():
+    """Test collector correctly handles multiple outputs by index."""
+    collector = RequestOutputCollector(RequestOutputKind.CUMULATIVE)
+    outputs = [
+        RequestOutput(
+            request_id="my-request-id",
+            prompt=None,
+            prompt_token_ids=[1, 2, 3],
+            prompt_logprobs=None,
+            outputs=[
+                CompletionOutput(
+                    index=0,
+                    text="a",
+                    token_ids=[0],
+                    cumulative_logprob=None,
+                    logprobs=None,
+                    finish_reason=None,
+                ),
+                CompletionOutput(
+                    index=1,
+                    text="b",
+                    token_ids=[1],
+                    cumulative_logprob=None,
+                    logprobs=None,
+                    finish_reason=None,
+                ),
+            ],
+            finished=False,
+        ),
+        RequestOutput(
+            request_id="my-request-id",
+            prompt=None,
+            prompt_token_ids=[1, 2, 3],
+            prompt_logprobs=None,
+            outputs=[
+                CompletionOutput(
+                    index=0,
+                    text="ab",
+                    token_ids=[0, 1],
+                    cumulative_logprob=None,
+                    logprobs=None,
+                    finish_reason=None,
+                ),
+                CompletionOutput(
+                    index=2,
+                    text="c",
+                    token_ids=[2],
+                    cumulative_logprob=None,
+                    logprobs=None,
+                    finish_reason=None,
+                ),
+            ],
+            finished=False,
+        ),
+    ]
+    for output in outputs:
+        collector.put(output)
+
+    # Get the output and check that the text and token_ids are correct.
+    result = await collector.get()
+    # We are expecting
+    # [{index: 0, text: "ab"}, {index: 1, text: "b"}, {index: 2, text: "c"}]
+    assert len(result.outputs) == 3
+    # First is the one where index is 0
+    first = [k for k in result.outputs if k.index == 0]
+    assert len(first) == 1
+    assert first[0].text == "ab"
+
+    # Second is the one where index is 1
+    second = [k for k in result.outputs if k.index == 1]
+    assert len(second) == 1
+    assert second[0].text == "b"
+    assert second[0].token_ids == [1]
+
+    # Third is the one where index is 2
+    third = [k for k in result.outputs if k.index == 2]
+    assert len(third) == 1
+    assert third[0].text == "c"
diff --git a/vllm/outputs.py b/vllm/outputs.py
index 014e8d5d8823..c8b9be5424e4 100644
--- a/vllm/outputs.py
+++ b/vllm/outputs.py
@@ -134,26 +134,32 @@ class RequestOutput:
         self.encoder_prompt_token_ids = encoder_prompt_token_ids
         self.num_cached_tokens = num_cached_tokens
 
-    def add(self, next_output: "RequestOutput") -> None:
+    def add(self, next_output: "RequestOutput", aggregate: bool) -> None:
         """Merge subsequent RequestOutput into this one"""
 
         self.finished |= next_output.finished
 
         for next_completion in next_output.outputs:
-            for completion in self.outputs:
+            for i, completion in enumerate(self.outputs):
                 if completion.index == next_completion.index:
-                    # Merge outputs with same index
-                    completion.text += next_completion.text
-                    if not isinstance(completion.token_ids, MutableSequence):
-                        completion.token_ids = list(completion.token_ids)
-                    completion.token_ids.extend(next_completion.token_ids)
-                    if next_completion.logprobs:
-                        assert completion.logprobs is not None
-                        completion.logprobs.extend(next_completion.logprobs)
-                    completion.cumulative_logprob = (
-                        next_completion.cumulative_logprob)
-                    completion.finish_reason = next_completion.finish_reason
-                    completion.stop_reason = next_completion.stop_reason
+                    if aggregate:
+                        # Merge outputs with same index
+                        completion.text += next_completion.text
+                        if not isinstance(completion.token_ids,
+                                          MutableSequence):
+                            completion.token_ids = list(completion.token_ids)
+                        completion.token_ids.extend(next_completion.token_ids)
+                        if next_completion.logprobs:
+                            assert completion.logprobs is not None
+                            completion.logprobs.extend(
+                                next_completion.logprobs)
+                        completion.cumulative_logprob = (
+                            next_completion.cumulative_logprob)
+                        completion.finish_reason = next_completion.finish_reason
+                        completion.stop_reason = next_completion.stop_reason
+                    else:
+                        # Replace the output with the new one
+                        self.outputs[i] = next_completion
                     break
             else:
                 self.outputs.append(next_completion)
diff --git a/vllm/v1/engine/output_processor.py b/vllm/v1/engine/output_processor.py
index 21e2a1aee4e2..d652b17e55b3 100644
--- a/vllm/v1/engine/output_processor.py
+++ b/vllm/v1/engine/output_processor.py
@@ -37,12 +37,9 @@ class RequestOutputCollector:
             self.output = output
             self.ready.set()
         elif isinstance(self.output, RequestOutput):
-            if self.aggregate:
-                # Coalesce the outputs in delta case.
-                self.output.add(output)
-            else:
-                # Just replace latest in non-delta case.
-                self.output = output
+            # This ensures that request outputs with different request indexes
+            # (if n > 1) do not override each other.
+            self.output.add(output, aggregate=self.aggregate)
 
     async def get(self) -> RequestOutput:
         """Get operation blocks on put event."""