Absolutely possible, I’ve done it multiple times. Get a letter from your psychiatrist/other doctor, sign lease, give letter to landlord after lease has been signed.

Letter should say you need an animal to help your condition (shouldn’t have to specify the condition) and ideally should name the law that requires they allow it, the Fair Housing Act (depending on your state there may also be a relevant state law.

They’re not allowed to prohibit pets or charge pet rent or pet “deposits” (pet deposits aren’t usually refundable, they’re just fees). You are responsible for the cost of damages your pets do, but that’s always the case.

May be more difficult for 2 cats, but when you already have one it’s not hard to hide a second one.