This is my idea:
AWDs can live like packs. If possible, packs can border one another. For this, let's pretend me and Rosey border each other.
Let's say we each have territories size 3. This could be the default size.
Our packs can hunt and patrol and mark our territories.
Let's say I have lead AWDs named Winnie and Kodiak, and Rosey's alphas are Bella and Ace.
Now, let's say that you need to mark your territory every 12 hours. Let's say Rosey hasn't logged on yet and hasn't marked her borders.
Now, if I go patrol by that border, I can do one a few options.
I can hunt on her territory. If I successfully hunt, Rosey will get an alert about it. If not, when she goes to patrol she'll be able to scent my pack's smell on her territory.
I can move a few inches in to mark, kind of as a challenge or warning.
Or I can just mark my border normally and go home.
Now, Rosey and I can attempt to attack each other. Let's say I attack Rosey and I win. My territory will increase in size and hers will decrease. Now my territory is size 4 and Rosey's is size 2.
Let's say I'm successful and claim the rest of Rosey's territory. Mine will be size 6 and Rosey's will be 0. Rosey has no more territory - she's chased out and needs to find new territory. It will be the default size 3.
Of course, you wont be able dominate your neighbors. Although, the higher level and higher stats your lead AWD has, the more of a chance you'll get territory.
Of course, this isn't final. Just a suggestion.
So along with breeding and getting the best pack, you can also try to get the biggest territory.
Also, maybe every month, the AWD packs can meet for a peaceful gathering, like the gathering in the Warriors series. During this day or period of time, packs cannot attack each other and go about in peace. Maybe female battles can go on, or contests for the best AWDs, etc.
Just adding in goal suggestions.