If the vet rules out UTI, you may want to start anew with a brand new litter box and a different brand of litter . . . even consider the depth of the litter, as some cats prefer shallow and others like to dig to China . . . inappropriate elimination is one of the (if not THE) foremost reason people relinquish their cats, so kudos to you for trying to get to the bottom of this issue . . . my best wishes for success in correcting the problem.