The most cats we have ever had at one time was two. We have toyed with the idea of three but we live in the city so we don't have a lot of space and didn't think it would be fair to have three cats living in close quarters. Additionally we have a dog so a dog and two cats in the city is sort of pushing it. I have a friend who fosters and she always has at least 20 cats at a time, the most she ever has was 33 and they keep her busy. The best part is that she tends to find all of them forever homes and the ones she can't place she keeps.
