Hello again Carol,
OK, well it is going to take some time for sure. Most cats don't accept another cat for at least 6 months. And the end result may be that they may never be buddies, but you may achieve some peace in the house.
Some tips:
1) you should have 5 litterboxes! that is one for each cat and then one more. This will help any of the cats who are not wanting to interact be able to make it to a box without problems.
2) I recommend having a food bowl in each room with a little food in each. If you find this too difficult, then have one at counter height, one on the floor and one in another part of the apartment (bathroom, bedroom).
3) water bowls should be even dispersed as well
4) play with the new cat until she is exhausted. She may have to use you as the playmate for now. I would get some laser light toys, "fishing poles", balls, paper sacks, whatever you think she will play with. Who knows, maybe your other cats will play too?
5) You can always try some Feliway pheromone aerosols in the apartment to help alleviate some stress in the other cats. It isn't cheap, so if it doesn't look like its working within a month or two, it probably won't do much after that.
6) Tincture of time will help a lot. I know that is the hardest, but cats are fickle creatures and it takes them some time to accept a new "addition".
Good luck! Keep at it. The website veterinarypartner.com also has some great articles about cat behavior.
Sincerely,
Dr. Amanda
Dr. Amanda
Small Animal Veterinarian
Special interest in canine and feline behavior.