Are things like follow-up questions or duplicate questions if there were no satisfactory answers, permissible on this site?
No. If its your own question, a bounty is the right way, assuming you have the reputation. If you want to add more helpful, relevant details, go ahead (Thats to say, don't edit to bump. Edit to include more relevant information).
If its a related tangential question, sufficiently distinct to warrant its own question, you can refer back to the old one, but if you're trying to get attention by re-asking, no, thats not the best way to do it