A directory which I own and can write to contains hard links to files that I don't own and don't have write permission for. I want to open and edit these files in Emacs. When I save my changes, Emacs should rename the existing hard link by appending ~, then write my new version of the file as a new file owned by me.

I was under the impression that Emacs could just do this (because of the way it does backups), but it's not working; when I save, it attempts to change the file's permissions in order to write to it (and fails because I don't own the file). How do I make this happen?