I have a feeling they may do alliance brawls. I saw in another thread someone accidentally stumbled onto a funky page with the brawl stuff on it, but it disappeared when they went back. I assume they are testing it out. I have no idea how it would function and its likely just going to be each individual player against each other (5v5 or 3v3 with one player controlled hero each). But thats just my guess on it. Would be fun to see for sure.
Edit: here is the other post ‘mentioning’ alliance wars: Somebody Gotta Explain This