Like alchemists seeking the philosopher’s stone, improvisers have pursued the ideal of a fully improvised two-act play. Of course, the very notion may be chimerical: generating plots that are both complex and coherent seems almost beyond the pale of “yes, and” technique, and improv’s dreamy associative mechanisms tend to lock up when grounded in a single stable reality. But when a bona fide genius like T.J. Jagodowski takes command of the proceedings, anything is possible. The night I attended Play he was in rare form, owning the first act as an eventual murder victim, then stealing the second as a flaming latecomer to a drolly Agatha Christie-esque scene of intrigue. Ably supported by Dan Bakkedahl, Jet Eveleth, Debra Downing, and others, with producer Damian Arnold as onstage copilot, Jagodowski was a constant spur to the narrative momentum, then deftly brought things to a satisfying conclusion just as they were beginning to unravel. I still can’t say it was quite a play, but it was the closest thing to one I’ve seen yet on an improv stage. Open run: Tue 8 PM. ImprovOlympic, 3541 N. Clark, 773-880-0199. $10.