Living with multiple dogs is great if the dogs all get along. I’ve enjoyed the luxury of four-dog pack harmony for years now. But that’s not always the case. When I was growing up, we had three dogs and one of them habitually tried to eat the other two. It was scary. I can report from personal experience that living with dogs that don’t get along is a stressful nightmare.
Fortunately, behaviorists understand more about inter-dog aggression than they used to way back when. Basically, you and your dogs form a pack, and every dog knows where he stands in the pack hierarchy. Problems often arise when humans try to interfere with the pack order. In the canine world, there is no such thing as democracy or "fair." A pack has a dominant dog (alpha), second (beta), and so forth down to the last (omega) dog.
Generally, the dogs themselves determine pack order. The order generally hinges on personality, age, time in the pack, sex, and size. For example, even though our dog Leto is the newest member of our pack, he’s still the dominant dog because he’s a male and much larger than the next largest dog. Cami is the beta dog, because she’s the most dominant of the three female dogs.
What many humans don’t understand is that to retain pack harmony, you need to do two things. One is that you should be UltraAlpha. Even the most dominant dog needs to respect you as the ultimate leader. Garnering respect isn’t about literally dominating the dog in any mean or physical way. Instead, you always make the dog "work" for any desired result, such as sitting before being petted or fed.
Secondly, you need to reinforce the pack hierarchy. If you coddle the omega dog, the alpha dog may view that as competition. With humans, there’s a tendency to "root for the underdog" so they want to console the omega when things don’t go her way. Ignoring the dominant dog in favor of the omega destabilizes the pack and can be the source of fights, as the alpha takes matters into his own hands (or paws).
When adding a new dog to your household, you should carefully consider how the new pack order will play out. Think about compatibility. If you have a very elderly shy dog, bringing home a boisterous, hyperactive dog is probably not a good idea. Also always introduce the new dog to the old dog on neutral territory. Many times the dogs will immediately figure out that they like each other. Or not.
Even if the dogs seem to basically get along, be prepared for a few squabbles especially in the initial phase until the hierarchy is completely settled. Don’t interfere as they sort things out. Generally the pack order will restabilize. Again, supporting the "loser" can have a destabilizing effect. Feed the dominant dog first and pay special attention to him to reinforce the hierarchy.
If it seems like the problems can’t be resolved, talk to your vet. Sometimes illness causes one dog to become a target. If the problem is serious, call in a professional behaviorist and be prepared to find a new home for one of the dogs.