I have four cats and two dogs. It is a zoo at my home and I love it. While I am not a veterinarian, I am pretty good at the day-to-day routines and nuances of having and taking care of multiple pets. It is very important to carefully and slowly introduce a new pet to the other pets in the home.
Before you make the choice to bring in a new pet, consider the personalities of your existing pets. If any of them are particularly aggressive, please make this move slowly. If done properly, you may be able to accomplish this successfully. You should also be careful if you have an especially meek or introverted pet, you do not want to scare him and cause him to withdraw more.
Some easy methods for introduction:
Let them sniff and inspect each other, but watch them carefully
Be ready to separate them if necessary
Start with small increments of time together
Do not leave them alone together if you see signs of aggression or hostility
Use gates if necessary
For dogs, try to walk them together, if possible
Feed them separately
Be on hand with a stern voice and a water quirt bottle
Give all of the babies lots of love and attention
Evaluate their behavior periodically
The settling in period should last from 4-6 weeks
If aggressive behavior continues after six weeks, you may have problem. You have to consider the health and well being of all the pets. Some pets are best being in a single pet home. Too many pets simply overwhelm them.
In the world of pets there will be always be a dominant one. This is okay if the dominance is not hurting the other pets. My youngest and newest dog is the boss, but her bossy ways are harmless and non-threatening. She is just a princess.
Go slowly, be present, give lots of love to all the pets, and evaluate often when introducing a new pet to your home. Good luck!