This is just a bit of though experiment of mine regarding the rules of chess. Enjoy!
While a pawn can only capture en passant once in today's rules, as @Seth points out in his wonderful answer, it wasn't always so cut and dry in the 19th century. Many joke compositions have been made that exploited the fact that you could apparently promote to an enemy piece. However, promotion into an enemy pawn is a bit unclear, because there is no rule on how a pawn on a player's first rank would move.
But I think that since a player use to be able to not promote a pawn and keep it frozen on the 8th rank, it makes sense to me that a pawn on the first rank should simply be able to move forward. Since it would be it's first move, it would make sense to also grant it a double step. Lichess's supported chess variant Horde Chess allows it for the the first rank white pawns, as an example.
As such, if you could consider a pawn that promotes into an enemy pawn as the same pawn after the promotion, then a pawn could capture en passant twice. It's also a slight matter of chess semantics as well when it comest on considering it the same pawn.
Firstly, the black pawn captures a white pawn en passant and goes to the 7th rank.
[FEN "4k3/6p1/8/8/6p1/8/7P/4K3 w - - 0 1"]
1. h4 gxh3 2. Ke2 h2 3. Ke1
Since an illegal promotion to an enemy pawn can't be shown, let's presume that it happened. The black pawn moves onto the 8th rank and promotes into a white pawn. The new white pawn advances and captures a black pawn en passant. (I can't show it having a double step from the first rank, unfortunately.)
[FEN "4k3/6p1/8/8/8/8/8/4K2P w - - 0 1"]
1. h2 Ke7 2. h3 Ke8 3. h4 Ke7 4. h5 g5 5. hxg6
Now you have seen a pawn capture en passant twice, given that you bend the rules a little, an if the promoting pawn is considered the same pawn afterward.