Let me try to get this straight. For each part of a turn, both players get to hold priority at least once? So for the beginning phase for example, there is always a minimum of six transfers of priority (two for the untap, upkeep, and draw)? And if so, could you play something like a Mistbind Clique on your opponent's upkeep and tap down all their lands for their turn?
I hope my questions make at least a little sense.