Generally laws limiting the number of companion animals one can keep are local, not state. Although we do not track local laws, I recently read that Alderman Ray Suarez introduced legislation allowing only five dogs per home in Chicago. The article mentions nothing about cats. I suggest you contact his office or your local humane society for more information. Other municipalities in Illinois do have cat limit laws.

New York's dangerous dog law specifically states that while municipalities may adopt their own programs to regulate dangerous dogs, no such program shall regulate dogs in a manner that is specific to breed. Nevertheless, a few municipalities in NY have laws regulating the keeping of pit bulls and other breeds. I don't know if they are enforced and they might not be upheld if challenged. In the Village of Hempstead, for example, there is a provision that includes pit bulls within the definition of vicious dogs and then requires owners of vicious dogs to have insurance. New York City does not have a ban except that pit bulls are banned in NYC Public Housing Authority apartments, as are other dogs over 25 pounds. No-pet clauses are also fairly common in leases for apartments in NYC. Some insurance companies also refuse to issue policies to people with pit bulls, cancel a policy, or place restrictions. Although I cannot attest to the accuracy of the website, there is more information on local laws at www.rott-n-chatter.com . People with disabilities have additional rights to keep pets, regardless of breed specific laws.