When I have introduced new cats to the residents, I have kept the new cat/cats in a seperate room, then put the newby/ies in a cage in the room with the residents, (with part of the cage covered so the others can't poke in. This got them used to the presence of each other.
Then I gradually let the kitten out with the others for supervised play, lengthening the time together (unless there were signs of hostility, e.g. growling, hissing, etc.) in which case I shortened the time next encounter.
The easiest to introduce was the last. I had 4 kittens in from 5 weeks, first in one cage, then in two (as they grew larger.) They were in the cages in the common area with my 9 adult indoor cats (ranging from 1 year to 11.) The kittens got out to play in a 4' x 4' covered "cage" a few times a day, where the adults could see them (and walk over the top of the enclosure - not by my choice.) By the time I had found homes for 3 and decided to keep the reaining kitten, the cats were so used to her, I just let her out of the cage (to her ecstatic delight) and no one noticed or objected.
One of the kittens went to a friend with a well-behaved 3-4 year old lady cat. The rambunctious little kitten was regarded by her with horror. My friend borrowed a cage along with the kitten, and put the little guy back into the cage when his play got too much for the lady cat. It took a few months, and now the two are the best of friends, with mutual cuddling & grooming. (Kitten was fed seperately in the cage & had toys, litterbox & cushion within. However, no question he preferred all the lady cat's toys and his favorite toy was the lady cat.)