diff --git a/src/cleo/formatters/formatter.py b/src/cleo/formatters/formatter.py
index 0ac13118..d6d4fbd7 100644
--- a/src/cleo/formatters/formatter.py
+++ b/src/cleo/formatters/formatter.py
@@ -2,6 +2,7 @@
 
 import re
 
+from contextvars import ContextVar
 from typing import ClassVar
 
 from cleo.exceptions import CleoValueError
@@ -18,6 +19,9 @@ def __init__(
         self, decorated: bool = False, styles: dict[str, Style] | None = None
     ) -> None:
         self._decorated = decorated
+        self._decoration_suppressed: ContextVar[bool] = ContextVar(
+            "decoration_suppressed", default=False
+        )
         self._styles: dict[str, Style] = {}
 
         self.set_style("error", Style("red", options=["bold"]))
@@ -120,14 +124,11 @@ def format_and_wrap(self, message: str, width: int) -> str:
         return output.replace("\0", "\\").replace("\\<", "<")
 
     def remove_format(self, text: str) -> str:
-        decorated = self._decorated
-
-        self._decorated = False
-        text = re.sub(r"\033\[[^m]*m", "", self.format(text))
-
-        self._decorated = decorated
-
-        return text
+        token = self._decoration_suppressed.set(True)
+        try:
+            return re.sub(r"\033\[[^m]*m", "", self.format(text))
+        finally:
+            self._decoration_suppressed.reset(token)
 
     def _create_style_from_string(self, string: str) -> Style | None:
         if string in self._styles:
@@ -165,7 +166,7 @@ def _apply_current_style(
             return "", current_line_length
 
         if not width:
-            if self.is_decorated():
+            if self._should_decorate():
                 return self._style_stack.current.apply(text), current_line_length
 
             return text, current_line_length
@@ -193,8 +194,11 @@ def _apply_current_style(
             if current_line_length >= width:
                 current_line_length = 0
 
-        if self.is_decorated():
+        if self._should_decorate():
             apply = self._style_stack.current.apply
             text = "\n".join(map(apply, lines))
 
         return text, current_line_length
+
+    def _should_decorate(self) -> bool:
+        return self.is_decorated() and not self._decoration_suppressed.get()
diff --git a/tests/io/outputs/test_section_output.py b/tests/io/outputs/test_section_output.py
index 2a9fcabd..13eb159f 100644
--- a/tests/io/outputs/test_section_output.py
+++ b/tests/io/outputs/test_section_output.py
@@ -1,10 +1,14 @@
 from __future__ import annotations
 
 from io import StringIO
+from threading import Event
+from threading import Thread
 
 import pytest
 
+from cleo.formatters.formatter import Formatter
 from cleo.io.outputs.section_output import SectionOutput
+from cleo.io.outputs.stream_output import StreamOutput
 
 
 @pytest.fixture()
@@ -109,3 +113,40 @@ def test_multiple_sections_output(
         stream.read()
         == "Foo\nBar\n\x1b[2A\x1b[0JBar\n\x1b[1A\x1b[0JBaz\nBar\n\x1b[1A\x1b[0JFoobar\n"
     )
+
+
+def test_remove_format_does_not_change_shared_decoration_state() -> None:
+    entered = Event()
+    continue_run = Event()
+
+    class SlowFormatter(Formatter):
+        def format(self, message: str) -> str:
+            entered.set()
+            continue_run.wait(timeout=2)
+            return super().format(message)
+
+    stream = StringIO()
+    formatter = SlowFormatter(decorated=True)
+    output = StreamOutput(stream, decorated=True, formatter=formatter)
+    section = output.section()
+    result: dict[str, object] = {}
+
+    def worker() -> None:
+        result["text"] = section.remove_format("<info>x</info>")
+
+    thread = Thread(target=worker)
+    thread.start()
+    assert entered.wait(timeout=2)
+
+    result["output_during"] = output.is_decorated()
+    result["section_during"] = section.is_decorated()
+
+    continue_run.set()
+    thread.join(timeout=2)
+
+    assert not thread.is_alive()
+    assert result == {
+        "text": "x",
+        "output_during": True,
+        "section_during": True,
+    }