diff --git a/dream-server/extensions/services/dashboard-api/routers/extensions.py b/dream-server/extensions/services/dashboard-api/routers/extensions.py
index 9179549f6..267f0e00f 100644
--- a/dream-server/extensions/services/dashboard-api/routers/extensions.py
+++ b/dream-server/extensions/services/dashboard-api/routers/extensions.py
@@ -473,9 +473,15 @@ def install_extension(service_id: str, api_key: str = Depends(verify_api_key)):
 
     # Early check (non-authoritative, rechecked under lock)
     if dest.exists():
-        raise HTTPException(
-            status_code=409, detail=f"Extension already installed: {service_id}",
-        )
+        has_compose = (dest / "compose.yaml").exists()
+        has_disabled = (dest / "compose.yaml.disabled").exists()
+        if has_compose or has_disabled:
+            raise HTTPException(
+                status_code=409, detail=f"Extension already installed: {service_id}",
+            )
+        # Broken directory (no compose file) — clean up before reinstall
+        logger.warning("Cleaning up broken extension directory: %s", dest)
+        shutil.rmtree(dest)
 
     # Size check
     total_size = 0
@@ -492,10 +498,16 @@ def install_extension(service_id: str, api_key: str = Depends(verify_api_key)):
     with _extensions_lock():
         # Re-check under lock to prevent double-install race
         if dest.exists():
-            raise HTTPException(
-                status_code=409,
-                detail=f"Extension already installed: {service_id}",
-            )
+            has_compose = (dest / "compose.yaml").exists()
+            has_disabled = (dest / "compose.yaml.disabled").exists()
+            if has_compose or has_disabled:
+                raise HTTPException(
+                    status_code=409,
+                    detail=f"Extension already installed: {service_id}",
+                )
+            # Broken directory (no compose file) — clean up before reinstall
+            logger.warning("Cleaning up broken extension directory under lock: %s", dest)
+            shutil.rmtree(dest)
 
         USER_EXTENSIONS_DIR.mkdir(parents=True, exist_ok=True)
         tmpdir = tempfile.mkdtemp(dir=str(USER_EXTENSIONS_DIR.parent))
@@ -574,6 +586,9 @@ def enable_extension(service_id: str, api_key: str = Depends(verify_api_key)):
         for dep in depends_on:
             if not isinstance(dep, str) or not _SERVICE_ID_RE.match(dep):
                 continue
+            # Core services have compose in docker-compose.base.yml, not individual files
+            if dep in CORE_SERVICE_IDS:
+                continue
             # Check built-in extensions
             if (EXTENSIONS_DIR / dep / "compose.yaml").exists():
                 continue
diff --git a/dream-server/extensions/services/dashboard-api/tests/test_extensions.py b/dream-server/extensions/services/dashboard-api/tests/test_extensions.py
index 604ef6fac..9863f3644 100644
--- a/dream-server/extensions/services/dashboard-api/tests/test_extensions.py
+++ b/dream-server/extensions/services/dashboard-api/tests/test_extensions.py
@@ -395,6 +395,28 @@ def test_install_copies_and_enables(self, test_client, monkeypatch, tmp_path):
         assert (user_dir / "my-ext").is_dir()
         assert (user_dir / "my-ext" / "compose.yaml").exists()
 
+    def test_install_cleans_broken_directory(self, test_client, monkeypatch, tmp_path):
+        """Install succeeds when dest dir exists but has no compose files (broken state)."""
+        lib_dir = _setup_library_ext(tmp_path, "my-ext")
+        # Create a broken user extension directory (no compose.yaml or compose.yaml.disabled)
+        user_dir = tmp_path / "user"
+        user_dir.mkdir(exist_ok=True)
+        broken_dir = user_dir / "my-ext"
+        broken_dir.mkdir(exist_ok=True)
+        (broken_dir / "manifest.yaml").write_text("leftover: true\n")
+        _patch_mutation_config(monkeypatch, tmp_path, lib_dir=lib_dir,
+                               user_dir=user_dir)
+
+        resp = test_client.post(
+            "/api/extensions/my-ext/install",
+            headers=test_client.auth_headers,
+        )
+
+        assert resp.status_code == 200
+        data = resp.json()
+        assert data["action"] == "installed"
+        assert (user_dir / "my-ext" / "compose.yaml").exists()
+
     def test_install_already_installed_409(self, test_client, monkeypatch, tmp_path):
         """409 when extension is already installed."""
         lib_dir = _setup_library_ext(tmp_path, "my-ext")
@@ -514,6 +536,21 @@ def test_enable_already_enabled_409(self, test_client, monkeypatch, tmp_path):
         )
         assert resp.status_code == 409
 
+    def test_enable_allows_core_service_dependency(self, test_client, monkeypatch, tmp_path):
+        """Enable succeeds when depends_on includes a core service."""
+        manifest = {"service": {"depends_on": ["open-webui"]}}
+        user_dir = _setup_user_ext(tmp_path, "my-ext", enabled=False,
+                                   manifest=manifest)
+        _patch_mutation_config(monkeypatch, tmp_path, user_dir=user_dir)
+
+        resp = test_client.post(
+            "/api/extensions/my-ext/enable",
+            headers=test_client.auth_headers,
+        )
+        assert resp.status_code == 200
+        data = resp.json()
+        assert data["action"] == "enabled"
+
     def test_enable_missing_dependency_400(self, test_client, monkeypatch, tmp_path):
         """400 when a dependency is not enabled."""
         manifest = {"service": {"depends_on": ["missing-dep"]}}