Here’s the thing about plays. They follow a script. They have to. Tradition and licensing agreements insist. So Oedipus never turns down Jocasta. Laura’s glass unicorn always breaks. Hamlet is going to be A.B.D. forever.

But what if you could take a shredder to that final curtain? Imagine the shock when Mary Tyrone kicks morphine, when George and Martha funnel some black coffee into their guests and head to bed. I would pay a lot to see Godot show up.

It could happen. That’s the cockeyed promise of “Gravid Water,” a monthly show at the Upright Citizens Brigade Theater that puts trained actors and skilled improvisers into scenes together. The actors are handed copies of the script in advance and the improvisers aren’t. Then they’re shoved onstage together and have to muddle through as much dialogue as they can before the lights go down.

Last month, I caught my first “Gravid Water,” which was performed in U.C.B.’s new 42nd Street space, so new they still hadn’t removed any of the signage from the previous tenants, the Pearl Theater. Now that’s improv.