Quick Alchemy requires a SINGLE hand and it creates an elixir.
Then, at level 13, without altering Quick Alchemy elsewise, we can create 2 elixirs. Presumably, you're now holding 2 elixirs in the same hand (as an example, the other may have a shield, a weapon, a bomb, etc)
Then at level 17, we're now creating 3 elixirs. Again, still need ONE hand free.
So far, this seems RAW (and given that we can't have 3 hands ever, and we can create 3 elixirs, also RAI)
The question is though, if we can hold 2-3 elixirs in one hand, without this being stated as being part of the ability, but somehow handwaved as being an everyday, normal thing, why can't we normally also hold 2-3 elixirs either way? Or can we?
