I had this in my Ideas and Brainstorming folder. Might as well share it.
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Round 1: Joe play once, Mark play twice, Joe play once.
Round 2: Mark play once, Joe play twice, Mark play once.
It's always Joe, Mark, Joe, Mark, Joe, Mark... they alternate playing once and twice. In the first round, Joe might have the advantage of playing first but Mark get to play twice in a row, but Joe have the final word.
Yeah, go nuts. So far it looks like it could really work for your situation.