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Cat pee is a horrible thing. Even if I weren't deathly allergic, cat pee smell would keep me away from getting cats. One time a friend's cat peed on me while I was sleeping and it was very gross.
So I feel you. Consider this empathy, but I'm afraid I have no suggestions.
Once they've marked it, it's tough to stop them. Clean and Febreeze the heck out of the mattress and sofa cushions, flip them over if you can. (Not posting over there because I'm sure someone will say something similar but better, consider this an n-thing of that answer.)
When I brought home Baxter and Daisy, Baxter had some big-time inappropriate pee issues. The solution ended up being locking him up inside a very large (great dane-sized) vari-kennel with a cat bed and a litter box. After he was reliable about peeing in his box, I moved him, his bed and box to a bathroom and then a bedroom before releasing him to roam freely around the house. It was a pain in the ass (and took like 3 weeks) but he has been good since.
In retrospect, I think the root issue for Bax was he did not want to share a litter box. I'm not sure if isolating him past the dog kennel stage was necessary once I got an automated litter box.
Turtle is so cute! That's the kind of cat I think I would get if I were not allergic to them. Zuzu kinda freaks me out, something about its face being a little less cat-like and a little too... humanish?
Like you can tell (s)he's thinking.
Still cute though!
I have no suggestions--as I've never had this problem. But now I so want to go to PAWSChicago this weekend and interview new cats to go with the perfectly fine old ones, who don't really need another buddy.
When I adopted a feral I had the same problem. I ended up blocking him into the kitchen which had a small attached laundry area where the litter box was kept (food and water were in the kitchen part and my adult cat had no problem going over the barrier). He was in there during the day while I was at work and at night while I slept. That stopped once he could jump over the barrier (I can't remember what I used, might have been a baby gate), but by then he seemed to get the idea. While he was loose I tried to keep a good eye on him which wasn't too difficult (small apartment, closed the bedroom door, etc.). However, I agree with those at AskMe who say to check with your vet. She may have a UTI or something else going on. Another suggestion is to add another litter box if you're using only one.
Good luck and lots of kitty scritches!
PS: Have I mentioned how much Zuzu looks like my Abigail?
Ditto on the UTI and the marking. Even if you can't smell it, your cat can, and will continue to think of the marked item as "ok to pee here" as long as the scent lingers. I lost a brand new couch to just that problem. The only remedy for cat pee is burning. Sorry. :(