I work at a veterinary office, and have for 6 years. My suggestions are
1) Try pheromone treatments. Use a pheromone collars like NurturCalm on all the cats, to sooth the cats and make the move easier on all. There are collars & sprays, and wall plug-ins. They release a pheromone that is similar to the one released by the mother while she was lactating, it gives a calm soothing feeling to the cats. It usually takes ~48 hours for it to start working. Each collar last ~30 days. The Sprays & Collars ~$15-20 each, the Wall Plug-in ~$50 but works longer & better for a multiple cat house.
2) Switch bedding or something that smells like the other cat before moving letting them get acclimated to each others smell. switching items weekly so they still smell strong. Then the day before the new cat moves in put the other cat in a room all day, then when they move in remove the current cat & put the new cat in that room, and give the other cat the kennel that the other cats were moved in, to increase the acclimation to one another. When finally introducing them try to put one in a kennel so they can sniff noses but not hurt each other if either gets irritated. After a few hours you can let them out together but watch them closely the first few days.
3) Have one more litter box then you have cats (ex: 3 cats should have 4 litter boxes), and spread them throughout the house. There should also be at least 2 scratching posts. Cats can be very territorial of litter boxes & scratching posts and bully each other from using ones, the more opportunity they have to get to a litter box or use a scratching post, the less likely the are to use your floor, furniture, bed, or clothes for the deed.