Well rehoming is a solution but it's more difficult to find people that will care for this cat. You have to interview all the prospective people to determine which one would the best candidate to be the caregiver for Precious the cat.
There's another solution, look for the book Cat vs Cat mentioned in my post below. It explains how to introduce a new cat to an already established pet hierarchy in the household. It already does have a chapter on introducing a cat to a dog.