I can only confirm up to level 5 but I believe the maximum level is 6. From what I have seen so far the number of pieces is multiplied by 4 for every upgrade. Level 2 (4 pieces), level 3 (16 pieces), level 4 (64 pieces), level 5 (256 pieces) and level 6 if it exists will be (1024 pieces). Check out the Facebook tips page for this and more info on the game.
Paul Robson