diff --git a/dvc/utils/hydra.py b/dvc/utils/hydra.py
index 45fb759fd..5ee3180d4 100644
--- a/dvc/utils/hydra.py
+++ b/dvc/utils/hydra.py
@@ -1,4 +1,3 @@
-from collections import defaultdict
 from pathlib import Path
 from typing import TYPE_CHECKING, List
 
@@ -83,32 +82,21 @@ def to_hydra_overrides(path_overrides):
     return parser.parse_overrides(overrides=path_overrides)
 
 
+def dict_product(dicts):
+    import itertools
+
+    return [dict(zip(dicts, x)) for x in itertools.product(*dicts.values())]
+
+
 def get_hydra_sweeps(path_overrides):
-    merged_overrides = []
+    path_sweeps = {}
     for path, overrides in path_overrides.items():
-        # `.` is reserved character in hydra syntax
-        # _merge_ is required to support sweeps across multiple files.
-        merged_overrides.extend(
-            [
-                f"{path.replace('.', '_')}_merge_{override}"
-                for override in overrides
-            ]
-        )
-
-    hydra_overrides = to_hydra_overrides(merged_overrides)
-    for hydra_override in hydra_overrides:
-        if hydra_override.value_type == ValueType.GLOB_CHOICE_SWEEP:
-            raise InvalidArgumentError(
-                f"Glob override '{hydra_override.input_line}' "
-                "is not supported."
-            )
-
-    splits = BasicSweeper.split_arguments(hydra_overrides, None)[0]
-    sweeps = []
-    for split in splits:
-        sweep_overrides = defaultdict(list)
-        for merged_override in split:
-            path, override = merged_override.split("_merge_")
-            sweep_overrides[path.replace("_", ".")].append(override)
-        sweeps.append(dict(sweep_overrides))
-    return sweeps
+        overrides = to_hydra_overrides(overrides)
+        for override in overrides:
+            if override.value_type == ValueType.GLOB_CHOICE_SWEEP:
+                raise InvalidArgumentError(
+                    f"Glob override '{override.input_line}' "
+                    "is not supported."
+                )
+        path_sweeps[path] = BasicSweeper.split_arguments(overrides, None)[0]
+    return dict_product(path_sweeps)
diff --git a/tests/func/utils/test_hydra.py b/tests/func/utils/test_hydra.py
index 8d1c0d092..8338e3cbe 100644
--- a/tests/func/utils/test_hydra.py
+++ b/tests/func/utils/test_hydra.py
@@ -190,6 +190,15 @@ def test_compose_and_dump(tmp_dir, suffix, overrides, expected):
                 {"params.yaml": ["defaults/foo=2"]},
             ],
         ),
+        (
+            {"params.yaml": ["+foo=1,2", "~bar", "++foobar=5,6"]},
+            [
+                {"params.yaml": ["+foo=1", "~bar=null", "++foobar=5"]},
+                {"params.yaml": ["+foo=1", "~bar=null", "++foobar=6"]},
+                {"params.yaml": ["+foo=2", "~bar=null", "++foobar=5"]},
+                {"params.yaml": ["+foo=2", "~bar=null", "++foobar=6"]},
+            ],
+        ),
         (
             {"params.yaml": ["foo=1,2", "bar=3,4"]},
             [