What this site needs is a Clan Tournament.
A tournament just as any other except that you play in teams of three clan members (or any other number). There are several ways you can play a clan battle. One: each player plays (two games) against every member of the opposing clan. Two: the member with the highest rating plays against the member of the highest rating, the one with the lowest against the one with the lowest. You can award points just for winning from a clan, or you can let them depend on with what numbers you defeat the other clan. Of course your clan get clan points for winning from another clan.
Feel free to post suggestions or you opinion.