Correct me if I am wrong, but I believe they cannot in force a limit on how many pets you are allowed to have in a residence. I know they cannot in force the 'no pet policy' in apartments in Canada. My Grandmother was a manager at one and she told me this.
According to the Landlord and Tenant Board website, landlords are allowed to refuse to rent to someone with a pet. However, a “no pets” clause in a lease is void, so signing a lease that has one doesn't give your landlord the right to kick you out if you move an animal in.