How should I go about adding a new branch to an already existing story? Should I contact the original author to ask permission, or can I just go ahead and do it? The story I'd like to contribute to hasn't been updated since 2021, if that's relevant at all.
If it's moderated, sending the chapter to post is basically the same as asking for permission. If it's public you shouldn't need permission at all.
If the story hasn't been updated, you should check the Author's profile to see if they are still active on the site. If its Moderated and they have left, the chapter won't get approved. If the author has left the site, there's a thread where you can ask Friedman to let you take it over.