Is it possible to be in check by three pieces? Is it possible to be in check with three pieces?  My thoughts so far:

A normal move can't, due to the fact that you may only unblock one piece to make a discovered check, and then that piece may also threaten.
Castling also can't, due to the fact that when you castle you can't result in check (or even move through check).
Possibly en passant can, because you move one piece, and doing so may create a discovered check. Removing the pawn also creates a discovered check.
En passant also doesn't work. You can, potentially, discover two checks, one because the capturing pawn moves off a file and one because the removed pawn unblocks a diagonal. However, you can't simultaneously discover a check via the removed pawn and give check with the capturing pawn, because the only two squares threatened by the capturing pawn are a knight's move away from the removed pawn. So if the opponent's king is on one of these squares, it is not in line with the removed pawn. Consequently at most two checks can occur (either both discovered or one discovered and one normal).