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I've seen it recommended in many places that you should own a litter box for each cat in your home plus an extra. What are the reasons behind this, and is there an upper limit where this strategy stops helping?
Example from The Humane Society of the United States:
How many?
The general rule of thumb is one box for each cat plus one more. Then none of them will ever be prevented from eliminating in the litter box because it's already occupied.
According to this article on Pet Health Network, there is not really some special reason behind having an extra litter box - it is just for precautionary reasons. A dirty litter box could cause:
Cats are very territorial animals and might not want to share their litter box. So what happens when your cat's litter box becomes dirty and you are not around to clean it up? (The extra litter box comes in). An extra litter box can also give your cat variety of choices.
Inappropriate elimination (especially urination) is by far the most common problem folks have with indoor cats, and in most cases it can be resolved by adding more boxes. Collective experience tells us that N+1 usually seems to be sufficient, so the recommendation is to just start there and hopefully prevent any problems before they start.
Why? A few explanations I've seen:
Some cats will not use a box after another cat has. Some will defecate in a shared box but not urinate in it.
Some won't urinate and defecate in the same box even if they're the only cat.
Some will try to defend the boxes from use by others, and more boxes makes that impractical.
Some won't use a box that isn't clean enough, and more boxes means the waste is spread across more litter. (OTOH, if they're not picky, the same may mean you can clean them less often.)
Old or ill cats or young kittens may not be able to travel to a distant box in time, so having boxes spread around the home reduces the odds of an accident.
