Changes in Pack Order
When you have more than one dog, you will see your Chis develop a ranking from the Most-Powerful-and-to-be-Obeyed One (the alpha) to the I'll-Do-Anything-You-Say-If-You-Won't-Hurt-Me dog (the omega). In a large pack of dogs, you will find an alpha male and an alpha female. Though the female may appear to be the ultimate alpha, she's usually not. The supreme alpha male just puts up with her bossiness until he's had enough.
Pack Dynamics
If you have only two or three dogs in a home, the leader is generally the oldest dog or the one who's been with you the longest. The leader in a small-dog family could be either male or female and may actually be the smallest and physically weakest of your dogs. Age has its value in the dog kingdom.
Signs of submissiveness include submissive urination or defecation, rolling over on the back (exposing the belly), licking another dog's mouth, “smiling” (in which the dog exposes her teeth without aggression), allowing toys and chews to be taken away by the other dog, and lying down and waiting for the higher-ranking dog to finish eating before beginning her meal.
But the alpha position in a larger group of dogs can be tenuous. If among the pack there is a rising wannabe leader-of-the-pack, he will be looking for his chance to topple the alpha. If he sees any physical or mental weakening of the alpha dog (and this includes a health problem in the older dog that you're not yet aware of), you may see increasing irritability between the alpha and the beta dogs as the beta starts jockeying for position. This irritability may lead to arguments and possibly all-out fights with serious injuries.
What to Do
If you see the beginning of a power shift within your group of Chis, and you suspect the shift may not be a peaceful one, don't leave the two competing Chis alone together. Supervise them at all times, and prevent arguments by removing potential triggers, specifically, attention, food, chews, and toys. For example, don't praise, lavish love on, or punish one Chi when the other Chi is present. The Chi not receiving attention is likely to take exception to this and will jump in and attack the other Chi on the spot.
Make sure the sparring Chis are fed separately and don't have any opportunities to create issues over the last piece of kibble in a bowl. Give highly valued items, such as chews and favorite toys, to the Chis in their crates to enjoy.

