But swift as it moves and smart as it’s written, there’s head-scratching because we’re never given the actual names, ages, and present localities of these people; things are constructed tightly enough that unless you’re an expert on the Kennedy era, even tiny clues appear nowhere to be found. As the actors emerge from shadows at the top of the play, in fact, they acknowledge that the names have been changed to protect the geriatric. Just who are Brutus (Scott Glascock), Joe (Bill Dante), Trip (Buzz Roddy), Allen (Scott Van Tuyl) and Hildy (Charlotte Hampden)?

Over 24 scenes that are largely short, intense and revelatory, the actors also portray a constellation of stars from the glory days of Camelot. There’s Sam Rayburn, the speaker of the U.S. House of Representatives; Everett Dirksen, the Senate Republican leader; Lyndon Johnson, Kennedy’s vice president and successor; Nikita Khrushchev, the leader of the U.S.S.R.; George Smathers, a Democratic senator from Florida; Lee Harvey Oswald and Jack Ruby, the man the political establishment maintains shot Kennedy and the man who shot the shooter; J. Edgar Hoover, the cross-dressing head of the F.B.I.; plus a mob boss and others.

So the question is, does a group of stars equal a conspiratorial universe? The way director B. Peter Westerhoff stages certain scenes, I’m unsure. On the one hand, there are moments when staging, writing and acting coalesce so it seems evident that these people, whoever they are, were intimately involved or at least aware of the reasons behind, if not the plot behind, Kennedy’s assassination. If this is true, that would also raise the stakes dramatically in terms of the public’s right to know—it would be the key to unfurling the Warren Commission snow-job. On the other hand, there are moments when staging, writing and acting coalesce so you question whether the whole play is jerry-built fantasy fiction. If so, Stepp has created an alternate reality fertile enough to buy into. And if that’s the case, how about tackling 9/11 next?

The actors do their game best to add inferences and implications in the few places where the text falls short. Mostly, though, we’re intrigued, with a sleuth-like hunger for concrete morsels. And, as with every unsolved mystery, there are questions: Why has no one prominent, politically or otherwise, mentioned these individuals, or are they already known to us? Are there Kennedy-era figures that survive, like the president’s paramour, Judith Campbell Exner, who are still holding back information despite the interviews they’ve granted? Are the surviving civil rights leaders holding back, too? Why We Shot John! accomplishes its central goal—offering the “why” behind Kennedy’s death. Shall we now ask “why not”?

Runs through Oct. 1. Altered Stages,