diff --git a/docs/source/pyro.poutine.txt b/docs/source/pyro.poutine.txt
index f975759586..443b527ce6 100644
--- a/docs/source/pyro.poutine.txt
+++ b/docs/source/pyro.poutine.txt
@@ -54,6 +54,14 @@ ________________
     :undoc-members:
     :show-inheritance:
 
+EqualizeMessenger
+____________________
+
+.. automodule:: pyro.poutine.equalize_messenger
+    :members:
+    :undoc-members:
+    :show-inheritance:
+
 EscapeMessenger
 ________________
 
diff --git a/pyro/poutine/__init__.py b/pyro/poutine/__init__.py
index 6ea794c6bc..78d11a9655 100644
--- a/pyro/poutine/__init__.py
+++ b/pyro/poutine/__init__.py
@@ -8,6 +8,7 @@
     condition,
     do,
     enum,
+    equalize,
     escape,
     infer_config,
     lift,
@@ -36,6 +37,7 @@
     "enable_validation",
     "enum",
     "escape",
+    "equalize",
     "get_mask",
     "infer_config",
     "is_validation_enabled",
diff --git a/pyro/poutine/equalize_messenger.py b/pyro/poutine/equalize_messenger.py
new file mode 100644
index 0000000000..035d96c06b
--- /dev/null
+++ b/pyro/poutine/equalize_messenger.py
@@ -0,0 +1,77 @@
+# Copyright Contributors to the Pyro project.
+# SPDX-License-Identifier: Apache-2.0
+
+import re
+from typing import List, Optional, Union
+
+from typing_extensions import Self
+
+from pyro.distributions import Delta
+from pyro.poutine.messenger import Messenger
+from pyro.poutine.runtime import Message
+
+
+class EqualizeMessenger(Messenger):
+    """
+    Given a stochastic function with some primitive statements and a list of names,
+    force the primitive statements at those names to have the same value,
+    with that value being the result of the first primitive statement matching those names.
+
+    Consider the following Pyro program:
+
+        >>> def per_category_model(category):
+        ...     shift = pyro.param(f'{category}_shift', torch.randn(1))
+        ...     mean = pyro.sample(f'{category}_mean', pyro.distributions.Normal(0, 1))
+        ...     std = pyro.sample(f'{category}_std', pyro.distributions.LogNormal(0, 1))
+        ...     return pyro.sample(f'{category}_values', pyro.distributions.Normal(mean + shift, std))
+
+    Running the program for multiple categories can be done by
+
+        >>> def model(categories):
+        ...     return {category:per_category_model(category) for category in categories}
+
+    To make the `std` sample sites have the same value, we can write
+
+        >>> equal_std_model = pyro.poutine.equalize(model, '.+_std')
+
+    If on top of the above we would like to make the 'shift' parameters identical, we can write
+
+        >>> equal_std_param_model = pyro.poutine.equalize(equal_std_model, '.+_shift', 'param')
+
+    :param fn: a stochastic function (callable containing Pyro primitive calls)
+    :param sites: a string or list of strings to match site names (the strings can be regular expressions)
+    :param type: a string specifying the site type (default is 'sample')
+    :returns: stochastic function decorated with a :class:`~pyro.poutine.equalize_messenger.EqualizeMessenger`
+    """
+
+    def __init__(
+        self, sites: Union[str, List[str]], type: Optional[str] = "sample"
+    ) -> None:
+        super().__init__()
+        self.sites = [sites] if isinstance(sites, str) else sites
+        self.type = type
+
+    def __enter__(self) -> Self:
+        self.value = None
+        return super().__enter__()
+
+    def _is_matching(self, msg: Message) -> bool:
+        if msg["type"] == self.type:
+            for site in self.sites:
+                if re.compile(site).fullmatch(msg["name"]) is not None:  # type: ignore[arg-type]
+                    return True
+        return False
+
+    def _postprocess_message(self, msg: Message) -> None:
+        if self.value is None and self._is_matching(msg):
+            value = msg["value"]
+            assert value is not None
+            self.value = value
+
+    def _process_message(self, msg: Message) -> None:
+        if self.value is not None and self._is_matching(msg):  # type: ignore[unreachable]
+            msg["value"] = self.value  # type: ignore[unreachable]
+            if msg["type"] == "sample":
+                msg["fn"] = Delta(self.value, event_dim=msg["fn"].event_dim)
+                msg["infer"] = {"_deterministic": True}
+                msg["is_observed"] = True
diff --git a/pyro/poutine/handlers.py b/pyro/poutine/handlers.py
index 278f6a60f2..343b1a1f4b 100644
--- a/pyro/poutine/handlers.py
+++ b/pyro/poutine/handlers.py
@@ -74,6 +74,7 @@
 from pyro.poutine.condition_messenger import ConditionMessenger
 from pyro.poutine.do_messenger import DoMessenger
 from pyro.poutine.enum_messenger import EnumMessenger
+from pyro.poutine.equalize_messenger import EqualizeMessenger
 from pyro.poutine.escape_messenger import EscapeMessenger
 from pyro.poutine.infer_config_messenger import InferConfigMessenger
 from pyro.poutine.lift_messenger import LiftMessenger
@@ -301,6 +302,29 @@ def escape(  # type: ignore[empty-body]
 ) -> Union[EscapeMessenger, Callable[_P, _T]]: ...
 
 
+@overload
+def equalize(
+    sites: Union[str, List[str]],
+    type: Optional[str],
+) -> ConditionMessenger: ...
+
+
+@overload
+def equalize(
+    fn: Callable[_P, _T],
+    sites: Union[str, List[str]],
+    type: Optional[str],
+) -> Callable[_P, _T]: ...
+
+
+@_make_handler(EqualizeMessenger)
+def equalize(  # type: ignore[empty-body]
+    fn: Callable[_P, _T],
+    sites: Union[str, List[str]],
+    type: Optional[str],
+) -> Union[EqualizeMessenger, Callable[_P, _T]]: ...
+
+
 @overload
 def infer_config(
     config_fn: Callable[["Message"], "InferDict"],
diff --git a/tests/poutine/test_poutines.py b/tests/poutine/test_poutines.py
index 944d26988d..7e2f7cfa8e 100644
--- a/tests/poutine/test_poutines.py
+++ b/tests/poutine/test_poutines.py
@@ -755,6 +755,50 @@ def test_infer_config_sample(self):
         assert tr.nodes["p"]["infer"] == {}
 
 
+class EqualizeHandlerTests(TestCase):
+    def setUp(self):
+        def per_category_model(category):
+            shift = pyro.param(f"{category}_shift", torch.randn(1))
+            mean = pyro.sample(f"{category}_mean", pyro.distributions.Normal(0, 1))
+            std = pyro.sample(f"{category}_std", pyro.distributions.LogNormal(0, 1))
+            with pyro.plate(f"{category}_num_samples", 5):
+                return pyro.sample(
+                    f"{category}_values", pyro.distributions.Normal(mean + shift, std)
+                )
+
+        def model(categories=["dogs", "cats"]):
+            return {category: per_category_model(category) for category in categories}
+
+        self.model = model
+
+    def test_sample_site_equalization(self):
+        pyro.set_rng_seed(20240616)
+        pyro.clear_param_store()
+        model = poutine.equalize(self.model, ".+_std")
+        tr = pyro.poutine.trace(model).get_trace()
+        assert_equal(tr.nodes["cats_std"]["value"], tr.nodes["dogs_std"]["value"])
+        assert_not_equal(
+            tr.nodes["cats_shift"]["value"], tr.nodes["dogs_shift"]["value"]
+        )
+        guide = pyro.infer.autoguide.AutoNormal(model)
+        guide_sites = [*guide()]
+        assert guide_sites == [
+            "dogs_mean",
+            "dogs_std",
+            "dogs_values",
+            "cats_mean",
+            "cats_values",
+        ]
+
+    def test_param_equalization(self):
+        pyro.set_rng_seed(20240616)
+        pyro.clear_param_store()
+        model = poutine.equalize(self.model, ".+_shift", "param")
+        tr = pyro.poutine.trace(model).get_trace()
+        assert_equal(tr.nodes["cats_shift"]["value"], tr.nodes["dogs_shift"]["value"])
+        assert_not_equal(tr.nodes["cats_std"]["value"], tr.nodes["dogs_std"]["value"])
+
+
 @pytest.mark.parametrize("first_available_dim", [-1, -2, -3])
 @pytest.mark.parametrize("depth", [0, 1, 2])
 def test_enumerate_poutine(depth, first_available_dim):