Desperate Alliance reads:
Action: Choose a hero you control. Until the end of the phase, give control of that hero and all resources in that hero's resource pool to another player. (Limit 1 per phase.)
FAQ 1.51 reads:
When a card with a triggered effect has a limit on the number of times that effect can be triggered (i.e. “Once per round,” “Limit 3 times per phase,” etc.), the limit is specific to that card. However, if a card has a limit of “once per game,” that limitation is specific to the player who triggered it.
So what is the limitation on DA preventing me from doing then? The way I understand the FAQ, I can still play three copies of the card if I have them all in my hand. So I guess it is preventing me from doing something like playing DA, getting it back with Dwarven Tomb, then playing it again?
This further complicates things. What if I play DA, then Will of the West, then draw and pick up a DA? Is it the same card? I dunno...