Well, this is only my experience. I only have 4 litter boxes in my house. I have 1 in my bedroom and that one is used by 4-6 cats. Then my mother has one in her bedroom, and that is normally used by 2 cats, and then there is two in the kitten room used by my 7 foster kittens..and everyone else goes outside in the sand box, and flowerbeds..which I don't mind at all!
But I am sure you could use one box for three if you made sure it was always clean. But it would probably be a better idea to get another one. People recommend one per cat, PLUS one.
you need at least 4 cat boxes. They should be located in different parts of the house and kept very clean. Cats like choices, also, not a good idea for only one box, cats resource guard, keeping the other cat/s from using the box. A cat that is resource guarding lies in the middle of the hall or entrance to the room where the box is. The other cat/s don't dare walk by to use the box.
Marilyn Krieger, CCBC www.thecatcoach.com