Budapest is awash with Thai massage places… the seedier they look, the seedier they are. By all accounts almost all (except perhaps the very smartest) will offer a happy ending. BJ and sex are rarely on offer, and when they are the masseuse will never say as much until you are in the room.
For non-Thai massages, google “erotic massage Budapest”. These appear to be appointment only and some have delights such as milking tables. Again, it seems like HJ is the most you will get - unless you are lucky. Otherwise it’s independents, as other have suggested.