Is it possible for me to add commits to someone else’s pull request on a repository where I am not the owner?
e.g.
User A owns Project X.
User B
You cannot add commits directly to User B's pull-request unless you have write access to User B's fork. You can, however, make local additions to the pull-request, by just fetching the pull-request branch into your own local repo (assuming the url for B's fork is public).
I'm not sure if it's possible to do a pull-request into B's fork since your own fork is from A and not B, though.