Hello Dindin,
What I would suggest, is keeping the new cat in one room only for awhile, so the others can adjust to her smell. Keep cat interludes brief for a week or so, depending on how you think everyone is reacting. It's true that there will be some squabbling when it comes to organizing the dominance ranks, but once everything is sorted out, it will be more peaceful.
Be sure to give lots of attention and praise (maybe more than normal) to your other cats, so they don't feel like they will be ignored because of this new cat. Slowly introduce them. Maybe have the new cat on a leash and sit with her, while the others enter the room and see from a distance. Also, if it gets to the point where they are all cohabitating in the room, praise the other cats and give them treats whenever the new cat is around, so they will associate the new cat with good things
Be sure to let us know how it goes!!