Twice now I've introduced newcomers by keeping them separate for a long time first, and it's worked really well. Shut the newbie in an extra room. That place becomes hers, so she feels safe in a new environment and has a 'home base' to retreat to. And the current family doesn't feel so invaded -- they still have control of the whole house except for the one room with The Thing Behind The Door. Then just let it simmer. Expect two weeks at least.
Sniffing noses and eyeballs peering under the door give way to wide-eyed stares as you leave the door open when you go in to feed or hang out with the newbie. After a few days start leaving the door open so the newbie can wander into the main area when you're there to supervise. My most territorial cat was outside the first couple of times the newbie came out of the room and scouted the house, that helped too: the newbie could roam without getting jumped, and later the alpha cat could come in and smell the newbie around the house without having to deal with meeting her face-to-face yet. Soon the newbie started coming out of her room, and all the cats just hung out and oh-so-casually watched each other. After a few hours she'd wander back into her room, and I'd shut the door again so everyone could relax and digest that. Finally, after three weeks, I left the door open all night, and nobody complained. (It might have gotten there a week sooner, but I was out of town, so introductions were on hold while I was away.)
And this time I happened to end up with a big cardboard box on its side in the living room. It's perfect -- newbie comes out and hangs out in the box -- able to see everything, right smack in the middle of the family -- yet totally protected.
The key to this is small increments. Go slowly, don't push it. Never bring her out of the room, let her decide when she's ready to approach. Get bored with how anti-climactic it's becoming. Oh, and the newbie's door is ALWAYS open when she's in the main house -- she has to be able to retreat safely.
As I said, I've done it this way twice, and am amazed how well it works. The first time I hadn't intended for the cats to blend at all -- I was a guest -- so I did nothing to push them together. They just became aware of each other under the door, then could smell each other around the house, then the door just got left open more and more and finally there was no need to shut the door anymore.
The next time I blended cats I was too eager, with two new kittens, to bring them all together. I wasn't patient (the kittens were SO cute and I wanted them in the main house right away!!). It turned out to be a stressful, hissy, growly time for several weeks.
This time I kept newbie separated because she was so sick and frail. (See thread "found a kitty" on Lost and Missing Pets forum.) She needed to eat, sleep, and not have to defend herself. She's doing well now, slowly regaining her weight and health. It was easy to not rush the introductions. Granted, this strategy is REALLY tough to follow when the newbie is cute and frisky and you want to spend every waking moment with them!
The cardboard box in the living room is such a help! I'll leave it there for another day or so. The last two steps will be moving her food and litterbox to wherever they're going to end up, but I'm in no hurry with that either. ~Kimberly