Hi there, I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with cats and dogs. I'm sorry to hear that you're dealing with this frustrating problem with Max - I'll do my best to help.
If you haven't done so already, the first thing I would do is have Max evaluated by your veterinarian for health concerns - particularly diabetes, kidney disease, hyperthyroidism, and bladder infection and stones. As a middle aged - approaching senior - kitty, he could definitely have developed a medical issue that is driving the inappropriate urination. The most common complaint I see from owners of diabetic cats when they come in before diagnosis is exactly what you're describing - urinating outside of the litter box.
I know that you've likely tried some of these things, but for completeness sake I'm going to type out all of my thoughts on litter box issues in kitties in case I hit on any that are new to you.
Cats are super fastidious, so some are very sensitive to a dirty litter box. Some cats absolutely will not pee or poop in a box that's not immaculate, so watching the boxes for cleanliness is important. Cats also tend not to like hoods on their boxes (especially bigger cats - they get too cramped) so I always recommend removing hoods from boxes. Cats also don't like to eat and potty in the same place, so food and water dishes shouldn't be near the litter box. I'm glad to hear that you're already doing this.
The ideal number of cat boxes is the number of cats in the home PLUS ONE. Each box should be in a separate spot - a cat will look at two boxes right next to each other as one box, so spread them out. Make sure there's at least one box on each floor of your home too, in case stairs are an issue, perhaps for an older arthritic cat. Boxes should be far from very noisy or unpredictable areas. A washer or dryer or furnace kicking on at just the wrong time can startle a cat and turn them off from the box entirely.
It's also a good idea to try a new type of litter. I usually recommend ADDING a new box rather than changing any of the existing boxes. If you're using clumpable litter, I'd rotate through trying pine litter (Feline Pine), recycled newspaper litter (Yesterday's News), crystal type litters, or corn cob litter. Sometimes you'll find that he will like one of these new litters better.
If these things aren't working and the situation is really desperate, I'll consider allowing them to become an indoor/outdoor cat with time outside. If they want to go outside and like to be out there, it often alleviates or eliminates completely the urinating in the home. Obviously, this approach comes with its own set of risks, but IF the choice is to rehome or euthanize them or to allow them to have some outdoor time, I'd choose the latter in an appropriate neighborhood. I've actually done this with my own cat and it's solved our issue. This one requires some serious thought about what your cat and your neighborhood are like and what the potential risks are to him being outside.
I've had some success with pheromone products like Feliway or Comfort Zone. They are geared more toward behavioral marking but sometimes can have an overall anti-anxiety effect and help with litterbox issues.
Lastly, I would consider a course of anti-anxiety medication like fluoxetine. In many of my patients this alleviates or eliminates the problem. Social stresses in a multicat household or other anxiety disorders in cats will commonly manifest as house soiling. Very frequently my patients have much improved litter box habits when they are on an anti-anxiety medication.
Some people do consider giving their cats up to a shelter, which is a very tricky proposition. I've seen many cats come to the shelter with a history of "house soiling" who do not do it in their new homes. No idea why - but I do see it happen, so it is a possibility. Depending on the resources of the shelter, the kitty may or may not be put up for adoption. If they are really strapped for resources and don't have the space to keep them and assess them, they may have to call the kitty "unadoptable" which would put them in line for euthanasia - so I would discuss with them before you sign them over, if you end up needing to consider the shelter route.
As I said, I absolutely appreciate how difficult this problem is - I've been there myself and it breaks my heart. I miss having my cat in bed with me every night, but I also cannot have him peeing in my house. My dad is retired but he practiced as a vet for 50+ years. As you can imagine, his view on "house soiling" cats was pretty black and white - he used to say "they live in my house, not the other way around". But times have changed - they are such a part of our family that they are not disposable and we aren't going to just give up on them. I'm sorry that you're having to deal with this. Please let me know if I can elaborate on any of those individual things that I mentioned - as I'd be happy to do so :)
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