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.