I think that for some people even 2 can be too many, for others 10. It all depends on the situation. I think that you reach your limit when you can no longer offer the life they deserve: regular vet visits, proper food, good living conditions and some quality time with them.

I have 3 at the moment for a while, when my sister temporarily moved in with me, we had 5 and it wasn't much of a problem.