Purrley, every single rental I've ever lived in DOES limit the number of residents - it's standard to restrict the number to twice the bedrooms - a 3 bedroom unit would have a 6 resident restriction. Even if the association doesn't, your local municipality might.

Check into this. If there are indeed too many residents in some units, and the association refuses to enforce that rule, you MAY be able to legally prevent them from enforcing the pets rule.