Well like everyone else said here...as long as you can care for them then go for it, but cat vacinations are expensive and one cat can cost up to 300 dollars in all needed vacinations, so if you are on a limited budget, then yes you can have too many cats and they can get diseases. It happened to a friend of mine who had too many cats because she did not have the money to completely vacinate them all and many died of horrible diseases.
You can also have too many cats if you are unable to make sure they are all fed and well taken care of.
But on my end...we have always had a manegerie.
Right now, I have 2 dogs, a parrot, and 2 fish which I am comfortable with. We moved so we had to find homes for the other animals we had.
At one time, we had 4 rabbits, 23 chickens, 8 cockatiels, 1 cockatoo, 4 fish, 6 dogs, 2 snakes, 20+ hamsters (we got them when they were babies and were told that they were both female...uhhh nope), 5 breeder-feeder rats, 1 cat, 1 turtle, 1 goat (we had to give it back because the dogs kept chasing it)
The only ones I had trouble taking care of were 3 angora rabbits....their hair tangled so easily and were prone to infection.
I know from experience that this many animals is alot of work...it seemed all I had time for was to feed/water them but as far as personal time with each one of them...that was difficult.
My mom got "a little" carried away on animals....but then I was expected to take care of them.
The number we have now...I am able to give each of my animals individual time. Although I do like chickens.......
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All art is a kind of confession, more or less oblique. All artists, if they are to survive, are forced, at last, to tell the whole story; to vomit the anguish up.
-James Baldwin