diff --git a/dvc/exceptions.py b/dvc/exceptions.py
index 7623c31a44..ba3f8467e0 100644
--- a/dvc/exceptions.py
+++ b/dvc/exceptions.py
@@ -1,9 +1,12 @@
 """Exceptions raised by the dvc."""
 import errno
-from typing import Dict, List
+from typing import TYPE_CHECKING, Dict, List, Set
 
 from dvc.utils import format_link
 
+if TYPE_CHECKING:
+    from dvc.stage import Stage
+
 
 class DvcException(Exception):
     """Base class for all dvc exceptions."""
@@ -31,24 +34,25 @@ class OutputDuplicationError(DvcException):
         stages (list): list of paths to stages.
     """
 
-    def __init__(self, output, stages):
+    def __init__(self, output: str, stages: Set["Stage"]):
         from funcy import first
 
         assert isinstance(output, str)
         assert all(hasattr(stage, "relpath") for stage in stages)
-        msg = ""
-        stage_names = [s.addressing for s in stages]
-        stages_str = " ".join(stage_names)
         if len(stages) == 1:
-            stage_name = first(stages)
-            msg = f"output '{output}' is already specified in {stage_name}."
+            stage = first(stages)
+            msg = (
+                f"output '{output}' is already specified in {stage}."
+                f"\nUse `dvc remove {stage.addressing}` to stop tracking the "
+                "overlapping output."
+            )
         else:
-            msg = "output '{}' is already specified in stages:\n{}".format(
-                output, "\n".join(f"\t- {s}" for s in stage_names)
+            stage_names = "\n".join(["\t- " + s.addressing for s in stages])
+            msg = (
+                f"output '{output}' is specified in:\n{stage_names}"
+                "\nUse `dvc remove` with any of the above targets to stop tracking the "
+                "overlapping output."
             )
-        msg += (
-            f"\nUse `dvc remove {stages_str}` to stop tracking the overlapping output."
-        )
         super().__init__(msg)
         self.stages = stages
         self.output = output
diff --git a/dvc/repo/add.py b/dvc/repo/add.py
index 07cf83f7b8..4a1c580824 100644
--- a/dvc/repo/add.py
+++ b/dvc/repo/add.py
@@ -120,7 +120,7 @@ def translate_graph_error(stages: List["Stage"]) -> Iterator[None]:
         )
     except OutputDuplicationError as exc:
         raise OutputDuplicationError(  # noqa: B904
-            exc.output, list(set(exc.stages) - set(stages))
+            exc.output, set(exc.stages) - set(stages)
         )
 
 
diff --git a/dvc/repo/trie.py b/dvc/repo/trie.py
index 63b329e65a..f33aa34d56 100644
--- a/dvc/repo/trie.py
+++ b/dvc/repo/trie.py
@@ -14,7 +14,7 @@ def build_outs_trie(stages):
             # Check for dup outs
             if out_key in outs:
                 dup_stages = [stage, outs[out_key].stage]
-                raise OutputDuplicationError(str(out), dup_stages)
+                raise OutputDuplicationError(str(out), set(dup_stages))
 
             # Check for overlapping outs
             if outs.has_subtrie(out_key):
diff --git a/tests/func/test_add.py b/tests/func/test_add.py
index e340e64220..8503045bf8 100644
--- a/tests/func/test_add.py
+++ b/tests/func/test_add.py
@@ -12,7 +12,11 @@
 from dvc.cli import main
 from dvc.config import ConfigError
 from dvc.dvcfile import DVC_FILE_SUFFIX
-from dvc.exceptions import DvcException, OverlappingOutputPathsError
+from dvc.exceptions import (
+    DvcException,
+    OutputDuplicationError,
+    OverlappingOutputPathsError,
+)
 from dvc.fs import LocalFileSystem, system
 from dvc.output import (
     OutputAlreadyTrackedError,
@@ -22,7 +26,7 @@
 from dvc.stage import Stage
 from dvc.stage.exceptions import StageExternalOutputsError, StagePathNotFoundError
 from dvc.utils.fs import path_isin
-from dvc.utils.serialize import YAMLFileCorruptedError
+from dvc.utils.serialize import YAMLFileCorruptedError, dump_yaml
 from dvc_data.hashfile.hash import file_md5
 from dvc_data.hashfile.hash_info import HashInfo
 from tests.utils import get_gitignore_content
@@ -656,6 +660,25 @@ def test_try_adding_pipeline_tracked_output(tmp_dir, dvc, run_copy):
         dvc.add("bar")
 
 
+def test_try_adding_multiple_overlaps(tmp_dir, dvc):
+    tmp_dir.dvc_gen("foo", "foo")
+    dvcyaml_content = {
+        "stages": {
+            "echo-foo": {
+                "cmd": "echo foo > foo",
+                "outs": ["foo"],
+            }
+        }
+    }
+    dump_yaml("dvc.yaml", dvcyaml_content)
+    msg = (
+        "\nUse `dvc remove` with any of the above targets to stop tracking the "
+        "overlapping output."
+    )
+    with pytest.raises(OutputDuplicationError, match=msg):
+        dvc.add("foo")
+
+
 def test_add_pipeline_file(tmp_dir, dvc, run_copy):
     from dvc.dvcfile import PROJECT_FILE