I made a rough draft of a game but I haven’t been able to play it or refine it. It’s inspired by renga, the poetic tradition that lead to haiku. The structure is similar to telephone or telestrations.
Before the first round, everyone generates topics and puts them into a hat. In the first round, everyone draws a topic from the hat and they each have to write a three line, 5-7-5 syllable poem about it (without mentioning the topic by name). In the second round, everyone passes their haiku clockwise for the next person to write a couplet with 7-7 syllables. In the third round, the poems get passed a final turn and the last person adds another haiku-stanza to the end.