I'm sure this has been done before, but it occurred to me as well. (It's like the Kani Club activity "Words from the Heart" where the players add side commentary, sharing their true feelings out loud as if only the audience could hear them.)
Four people improvisation game.
Two people are the players, the other two are their shadows.
The two people meet each other for the first time. (The audience can choose a place beforehand.) They improvise a conversation, starting with a greeting.