diff --git a/vllm/model_executor/guided_decoding/xgrammar_decoding.py b/vllm/model_executor/guided_decoding/xgrammar_decoding.py
index 5b97f03257502..619263225333d 100644
--- a/vllm/model_executor/guided_decoding/xgrammar_decoding.py
+++ b/vllm/model_executor/guided_decoding/xgrammar_decoding.py
@@ -1,6 +1,7 @@
 # noqa: UP007
 from __future__ import annotations
 
+import copy
 import json
 from dataclasses import dataclass, field
 from typing import TYPE_CHECKING, Any
@@ -238,7 +239,6 @@ class XGrammarLogitsProcessor:
     token_bitmask: torch.Tensor = None  # type: ignore[assignment]
     matchers: list[xgr.GrammarMatcher] = field(default_factory=list)
     batch_size: int = field(default=1)
-    prefilled: bool = field(default=False)
 
     def __getstate__(self) -> dict[str, Any]:
         return {'config': self.config}
@@ -250,7 +250,6 @@ def __setstate__(self, state: dict[str, Any]):
         self.matchers = []
         self.batch_size = 1
         self.token_bitmask = None  # type: ignore[assignment]
-        self.prefilled = False
 
     def _ensure_ctx(self):
         """Lazily initialize the processor in the worker process"""
@@ -278,10 +277,7 @@ def __call__(self, input_ids: list[int],
             self.token_bitmask = xgr.allocate_token_bitmask(
                 self.batch_size, self.config.vocab_size)
 
-        if not self.prefilled:
-            # Have not sampled a token yet
-            self.prefilled = True
-        else:
+        if len(input_ids) > 0:
             for i, matcher in enumerate(self.matchers):
                 if not matcher.is_terminated():
                     sampled_token = input_ids[-1]
@@ -309,3 +305,7 @@ def __call__(self, input_ids: list[int],
             scores = scores.to(device_type).squeeze()
 
         return scores
+
+    def clone(self) -> XGrammarLogitsProcessor:
+        """Deepcopy due to per-sequence state in the matchers"""
+        return copy.deepcopy(self)
diff --git a/vllm/sampling_params.py b/vllm/sampling_params.py
index fc77f3ca529b2..605c09b8d7225 100644
--- a/vllm/sampling_params.py
+++ b/vllm/sampling_params.py
@@ -450,15 +450,16 @@ def all_stop_token_ids(self) -> Set[int]:
         return self._all_stop_token_ids
 
     def clone(self) -> "SamplingParams":
-        """Deep copy excluding LogitsProcessor objects.
+        """Deep copy, but maybe not the LogitsProcessor objects.
 
-        LogitsProcessor objects are excluded because they may contain an
-        arbitrary, nontrivial amount of data.
+        LogitsProcessor objects may contain an arbitrary, nontrivial amount of
+        data that is expensive to copy. However, if not copied, the processor
+        needs to support parallel decoding for multiple sequences
         See https://github.com/vllm-project/vllm/issues/3087
         """
 
         logit_processor_refs = None if self.logits_processors is None else {
-            id(lp): lp
+            id(lp): lp.clone() if hasattr(lp, 'clone') else lp
             for lp in self.logits_processors
         }
         return copy.deepcopy(self, memo=logit_processor_refs)
diff --git a/vllm/sequence.py b/vllm/sequence.py
index cc3d96fc93a79..15fe12aacb118 100644
--- a/vllm/sequence.py
+++ b/vllm/sequence.py
@@ -1366,9 +1366,9 @@ def maybe_assemble_group(
 class ParallelSampleSequenceGroup(SequenceGroupBase):
 
     @staticmethod
-    def add_request(request_id: str, engine, params, **kwargs):
+    def add_request(request_id: str, engine, params: Union[SamplingParams, PoolingParams], **kwargs):
         original_params = params
-        params = copy.deepcopy(original_params)
+        params = original_params.clone()
         params.n = 1
         group = ParallelSampleSequenceGroup(request_id)
         seqs = []