Had this thought while playing a tournament in which each pairing plays two matches.  What if you and your opponent played two games simultaneously, rolling two pairs of dice at a time.  You could choose which pair to apply to which game.  (Many variations suggest themselves, such as choosing two out of four for each game, etc., but let's stick with the basic idea for the moment.)  So, let's say the dice are 4-4 and 6-3.  I could use the 4-4 in either Game 1 or Game 2, but not both.  I would have to use the 6-3 in the other.  It might also be interesting to have a rule that you must use as many dice as possible, so that you could not assign dice in such a way that one or more could not be used, if there was another assignment that used more of them.