When we found ourselves in a similar situation last year, we did most of the same things people have mentioned. For the first few days the newcomer was quarantined in a room alone all day while the existing cat continued to have run of the house, and in the evening we let the new guy out for a while, until both of them seemed to have had enough. We gradually increased the time they were both loose until, after about two weeks, they were circulating freely. We continued to keep a separate litter box in the front room for a while, gradually moving it toward the “usual” litter box spot, and it was probably a month or more before we pared it back down to one. (My sister has three cats and still has multiple litter boxes, though, so you will have to judge from your own specimens whether they can adapt to using the same box or will continue to want two.) We still have, and plan to always have, two separate feeding stations in different rooms. Most of the time now they both eat from the same “main” bowls, but the “new” guy still goes to his bowls periodically, and I believe it is very valuable to both of them psychologically to have adequate food supplies that are physically separated so they don’t feel any instinctive pressure to compete/defend. (One of my sister’s cats grew up very small because the other cat would defend both bowls of food, which were adjacent, and drive the small cat off, even though they were litter mates.) Our existing cat was very sad for a while at the intrusion of the new guy into what she thought was her exclusive home, so be prepared for a period of cat depression (hopefully not angry acting-out behaviour). Be sure to really give extra attention to cat number one, even if, like ours, she turns her back on you for a while.
Other minor suggestions: Give them an opportunity to be at different levels in the house. Within one area we have (coincidentally) a standard chair, a high barstool-like chair, a pool table, and a flight of steps. The cats love this, as the rule seems to be that whoever is up higher gets to be dominant for the moment. At different times we found them in different spots, and over time they worked out a pecking order they could both live with (they take turns being number one cat). The point is that cats like to use that positioning thing as a means of getting established, so they will like it if you give them a means of gaining/giving up altitude; even if it’s just a temporary arrangement, it will help them sort out their dominance issues. Also, keep an eye on things when they first start spending time freely together, and if one cat is taking a consistent beating from the other (with us it was the old cat getting crap from the new one), step in when it looks like someone is getting a little stressed and tired of it. For us, that meant putting the new guy back in his room for a while and giving the old girl time to relax and roam without being pounced on.
As already mentioned, everyone will be tempted to fuss over the new guy, which is good for him, but make sure the established cat gets her equal share of it, particularly from you, the real parents (they aren’t as concerned about what visitors do, I find). Otherwise, you will undoubtedly already be doing the right stuff in advance - have all the physical tests done and new cat fixed, etc.
We had only one cat for many years and I was reluctant to have two, but having finally taken the step, I must say that you won’t be sorry. Even though I was very upset myself by how much the old cat seemed bothered by the new one at first, they will adjust soon enough and become friends on some level. Two really are twice as much fun as one, and double the cuteness. Bonus karma points for you for providing a good home to one more needy animal.
