how old are the dogs involved? sexes? intact or neutered? are we talking a true fight or just noisy disagreements?
if Dog A and B are both females and Dog B came into the house as a puppy, it's the normal time span that disagreements would begin. Adding a third dog can really stir things up, depending on the ages and personalities of the dogs involved.
This isn't really something that can be figured out over the itnernet. You need someone who is well versed in dog behavior and body language to observe the dogs in your home and find out what is triggering the fights. More than one person has thought "Dog A keeps fighting with Dog B" when actually Dog B is the one starting all the fights - Dog A was simply the first one making an obvious (to humans) aggressive move.