Well, considering my family and I do cat rescue, and I do rodent rescue..Our limit is quite a lot. We currently have 20 cats, and several fosters. Its hard finding homes for adult cats in a city where they are so plentiful. Our limit of cats is currently where it is. We have 1 foster cat that is pregnant, and after we rehome all the kittens to new homes, and the current fosters.>THEN we will bring in more fosters in need of homes.
As for my rodents, There are 13 rats (9 babies that are 16 days old), 5 hamsters, 5 mice (1 being pregnant), and 1 gerbil...I have the cage space, and my own "Rodent Room"..So its pretty good rodent wise. It takes a lot of time to properly socialize them all, and they ALL get out of cage time for atleast 2 hours a day. Not to mention, I give them the recommended diet for each (And I do the research on the appropriate care of these animals unlike a lot of people), and they have big spacious cages and lots of toys to help with their boredom when they are in their cage...
It takes commitment!
We have 13 dogs that are OUR dogs, and we don't have a foster dog and won't be having a foster dog. We are sticking to cat and rodent rescue for now. lol.
And then I have some reptiles and fish that my brother primarily cares for. (hes more of a skaley/shell type animal lover)
So i think it depends greatly on why you have so many pets, your space, how many people there are to help you take care of them...and honestly, if you have to money to afford to take care of them, and their vet bills.