It is pretty straight forward. the bonuses are rock which can one way attack scissors which can one way attack paper which can one way attack rock.
Discuss
How about 4 or 8 separate groups(continents) of scissors paper rock (inside which are one way attacks) and you have the option to bombard (rock to another group's scissors). bonus for holding whole group(continent). If i remember I'll do a pic.
If we are looking for more territories, how about the lizard-spock expansion. this is where spock beats rock and scissors (can attack those places) and is beaten by paper and the lizard. The lizard on the other hand beats spock and paper, but is beaten by rock and scissors. That will give you at least 5 territories (depending on if you add the 2 hands as territories or not). Just a thought.
We'd have to get our mars rover out of the crevasse first. That's exactly what got me thinking about this, lol. I don't think we should add it though, overcomplication. Isn't 3x8 enough? The entire idea seems a bit luck based though to me, it'd be hard to make a map of this where any strategy could exist.