Hi Sue,
I apologize for not responding before now. I have a 4-5 phase approach which usually works... it can take months, sometimes a year for some cats to integrate. I outline it in my book Naughty No More!

But, it's also important to know that there are some cats who refuse to accept another cat into the household. When that occurs, the best solution is to find the new cat another, fabulous home. It doesn't matter how attached one is to the cat or other circumstances--the priority is the health and well-being of the cats. Unfortunately, that is what happened here. One of my cats did not tolerate Pillow in the house. He threw himself against the door in an effort to reach Pillow. There was one serious incident of redirected aggression. I rehomed Pillow... with the person who adopted Pillow's best dog girl friend, Abby. There were also a couple of other cats who Pillow enjoyed hanging out with at the house. A wonderful home.