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.
Whenever they feel like it, the shadows can tap their players on the shoulder. When a shadow taps her player, the players pause, and the tapped player acts as if s/he were thinking. While s/he "thinks," the shadow says what s/he is thinking. The player then has to continue the dialogue based on what her shadow has said.
1: Hi, I'm Jackson, who are you?
2: I'm Mona. Nice to meet you. [tap]
Mona's shadow: "Jackson? Strange name. I wonder if I can trust him. Better to be careful."
2: So, Jackson. That's an interesting name. What do you do?
1: Well, [tap]
Jackson's shadow: "Should I tell her the truth or lie? The last person I told that I was a ninja spy secret agent, thought I was crazy."
1: I'm a plumber.