Edges cases wanted?
*You have 4 alchemists in play, an empty deck (but a non-empty discard pile) and you suspect that your opponent will play a militia next turn. In that case you might want to just put 3 alchemists back, because then - at the beginning of your next turn - your fourth alchemist will be in your deck instead of your discard pile.
*The current turn is a possession turn (and the next one will be the normal turn).
*You also have Scrying Pools, and you want as much non-actions in your hand as possible, because you're going to draw all actions more easily with scrying pool in that case. Or something similar with Herald.
*You want a specific other card in you hand. For example a curse to discard to opponent's mountebank, a province to reveal to opponent's tournament, a bane to reveal to opponent's YW, a crappy card in hand to trash to your opponent's Bishop, or any reaction card.
* You want to play other actions before you Alchemist chain. For example, Fishing Village + Library or Menagerie. Maybe you know these cards are on the top of your deck.