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 having trouble with Furssy - I will do my best to help.
The first thing I'd recommend doing here is having her to your vet for a good physical exam and potentially some blood work to make sure that there's not a health issue causing what you're seeing. A cat who is drinking a lot of water could be diabetic or have kidney issues, so before we call it a behavioral issue, we definitely want to make sure that she gets checked out for medical issues. The occasional vomiting could point to a medical issue or a dietary intolerance or even stress. If she's been cleared medically, that's when you can start working on potential behavioral issues. I don't know what all you've tried so far, so I'm going to include all that I know on the issue.
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. My favorite types of boxes are large low sided plastic storage containers. If your cat is able to climb over taller walled containers then you could also use a taller plastic bin to minimize litter being kicked out of the box. 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.
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. All of these litters have different smells and consistencies which some cats may like more or less. Sometimes you'll find that your cat will like one of these new litters better.
In a case where a cat is eliminating in just one specific place, there are a couple of different ways we can react. One would be to recognize that that the kitty is showing you their preference in location, so give them an acceptable option for pottying in that location by placing a cat litter box there or as close as possible to the offending spot. Obviously this is going to be more reasonable in some places than others in your house. The other way you could handle that would be to do something to make that particular place undesirable to the cat by placing something like packing tape, double sided sticky tape, plastic wrap, tin foil, or strong odored diffusers or sprays in the area. Sometimes this fixes the issue, but other times, unfortunately, this can backfire and cause the cat to just go find a new spot to use.
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. I've actually done this with my own cat and it's solved our issue. Since your kitty is aged, I don't think that this will be a reasonable option for you - it wouldn't likely be kind to put a 17 year old kitty outside at this point in her life.
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.
I hope that at least some of this is new and helpful info for you. Please let met know what questions I can answer for you. I'd also be happy to elaborate on any of these topics if you'd like - just let me know.
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