Internet sez: MOAR CATZ!!!
We shall see how long this lasts. My eyes are red and itchy. The cat is sneezing. We'll see who is more allergic to whom.
Worst case, the cat will go back to where it came from. It came from a family with three other cats, all of which were beating it up to the point where it was banished to be an outside-only cat. It was living in a basket (with a heating pad) on their (non-enclosed) porch.
Cat is currently roughly nine years old. It has an appointment at the vet in about two weeks.