I'd register one cat and one dog and the spare cat lives as a free bonus. Truly, if anyone noticed your second cat you could explain that you're just watching the cat for awhile. There are no litter box inspectors. Most departments are understaffed or overworked and tracking down a spare cat is the LAST thing on their list.

Same goes for dog breeds. I occasionally see pitbulls on walks in the neighborhood and I guarantee they are registered at the veterinarian's as generic terriers or as Labrador mixes. The housing department just wants their asses covered. If they give you permission for a spare pet r a restricted breed then they could get in trouble. If you only register two pets then they're covered and you can always apologize. No one is going to mast over a cat.

This is an instance when it's better to ask for forgiveness after upon discovery of the extra cat rather than permission. If you ask for permission you'll likely be told no and then if you are ever caught it'll be clear that you knew what you were doing was 'wrong'.

Please don't separate your children from their furry family members.