diff --git a/scmrepo/git/backend/base.py b/scmrepo/git/backend/base.py
index 118b54f7..0feef3ef 100644
--- a/scmrepo/git/backend/base.py
+++ b/scmrepo/git/backend/base.py
@@ -218,6 +218,7 @@ def push_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
@@ -228,6 +229,11 @@ def push_refspecs(
             refspecs: Iterable containing refspecs to fetch.
                 Note that this will not match subkeys.
             force: If True, remote refs will be overwritten.
+            on_diverged: Callback function which will be called if local ref
+                and remote have diverged and force is False. If the callback
+                returns True the remote ref will be overwritten.
+                Callback will be of the form:
+                    on_diverged(local_refname, remote_sha)
         """
 
     @abstractmethod
@@ -236,6 +242,7 @@ def fetch_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
@@ -247,6 +254,11 @@ def fetch_refspecs(
             refspecs: Iterable containing refspecs to fetch.
                 Note that this will not match subkeys.
             force: If True, local refs will be overwritten.
+            on_diverged: Callback function which will be called if local ref
+                and remote have diverged and force is False. If the callback
+                returns True the local ref will be overwritten.
+                Callback will be of the form:
+                    on_diverged(local_refname, remote_sha)
         """
 
     @abstractmethod
diff --git a/scmrepo/git/backend/dulwich/__init__.py b/scmrepo/git/backend/dulwich/__init__.py
index b45680b8..eff02942 100644
--- a/scmrepo/git/backend/dulwich/__init__.py
+++ b/scmrepo/git/backend/dulwich/__init__.py
@@ -493,6 +493,7 @@ def push_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
@@ -533,8 +534,16 @@ def update_refs(refs):
                         check_diverged(self.repo, refs[rh], self.repo.refs[lh])
                     except DivergedBranches:
                         if not force:
-                            change_result[refname] = SyncStatus.DIVERGED
-                            continue
+                            overwrite = (
+                                on_diverged(
+                                    os.fsdecode(lh), os.fsdecode(refs[rh])
+                                )
+                                if on_diverged
+                                else False
+                            )
+                            if not overwrite:
+                                change_result[refname] = SyncStatus.DIVERGED
+                                continue
 
                 if lh is None:
                     value = ZERO_SHA
@@ -556,7 +565,8 @@ def update_refs(refs):
                 ),
             )
         except (NotGitRepository, SendPackError) as exc:
-            raise SCMError(f"Git failed to push ref to '{url}'") from exc
+            src = [lh for (lh, _, _) in selected_refs]
+            raise SCMError(f"Git failed to push '{src}' to '{url}'") from exc
         except HTTPUnauthorized:
             raise AuthError(url)
         return change_result
@@ -566,6 +576,7 @@ def fetch_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: Optional[bool] = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
@@ -629,8 +640,18 @@ def determine_wants(remote_refs):
                     )
                 except DivergedBranches:
                     if not force:
-                        result[refname] = SyncStatus.DIVERGED
-                        continue
+                        overwrite = (
+                            on_diverged(
+                                os.fsdecode(rh),
+                                os.fsdecode(fetch_result.refs[lh]),
+                            )
+                            if on_diverged
+                            else False
+                        )
+                        if not overwrite:
+                            result[refname] = SyncStatus.DIVERGED
+                            continue
+
             self.repo.refs[rh] = fetch_result.refs[lh]
             result[refname] = SyncStatus.SUCCESS
         return result
diff --git a/scmrepo/git/backend/gitpython.py b/scmrepo/git/backend/gitpython.py
index bafc588d..5d4adb6a 100644
--- a/scmrepo/git/backend/gitpython.py
+++ b/scmrepo/git/backend/gitpython.py
@@ -479,6 +479,7 @@ def push_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
@@ -489,6 +490,7 @@ def fetch_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
diff --git a/scmrepo/git/backend/pygit2.py b/scmrepo/git/backend/pygit2.py
index 6fdef3a9..58e6e3b0 100644
--- a/scmrepo/git/backend/pygit2.py
+++ b/scmrepo/git/backend/pygit2.py
@@ -419,6 +419,7 @@ def push_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]:
@@ -429,6 +430,7 @@ def fetch_refspecs(
         url: str,
         refspecs: Union[str, Iterable[str]],
         force: bool = False,
+        on_diverged: Optional[Callable[[str, str], bool]] = None,
         progress: Callable[["GitProgressEvent"], None] = None,
         **kwargs,
     ) -> Mapping[str, SyncStatus]: