The text of Church says "Set aside up to 3 cards from your hand face down. At the start of your next turn, put them into your hand, then you may trash a card from your hand."
http://wiki.dominionstrategy.com/index.php/Church says "If you play Church multiple times such as via Throne Room, keep the set aside cards separate; you may not trash multiple cards from one set of cards."
OK, so "keep the set aside cards separate" makes sense, but I fail to see how "you may not trash multiple cards from one set of cards" can be correct.
At the start of your next turn you first pick up one of the sets of set-aside cards and trash any card that is now in your hand. Obviously that includes the cards that you have just picked up. Then you pick up the second set of set-aside cards and trash any card that is now in your hand. That includes not only the cards that you have just picked up, but also the cards you previously picked up, so demonstrably it is possible to trash multiple cards from one set of cards.