The stars supply most of the fireworks in “Meteor Shower,” a scattershot – and even scatterbrained – comedy of bad manners by Steve Martin at the Booth Theatre. The cast member whose presence is undoubtedly fueling the heat at the box office is of course Amy Schumer, the fearlessly and delightfully vulgar comic and star of her own television series. But her trio of co-stars – the television and film name Keegan-Michael Key, alongside theater veterans Laura Benanti and Jeremy Shamos – also provide plenty of assured comic acting. They all help spackle over the jagged holes in Martin’s play about two couples who gather for a night of stargazing that turns unexpectedly combustible, sexually and otherwise.

As the title suggests, it’s not just your everyday constellations that Corky (Schumer) and her husband Norm (Shamos) have invited his casual friend Gerald (Key) and his wife Laura (Benanti) to view. Corky and Norm live in Ojai in Southern California, which offers a less light-obscured view than Gerald and Laura would have in the more populous Santa Barbara. They have mutual friends (sort of) in a couple referred to as the Coopers, a phone call from whom figures prominently in the proceedings.

As they await the arrival of their guests, Corky and Norm sip a little “pre-wine,” as Corky calls it, and we see indications that there are slight fissures of tension in their marriage. Mainly this is indicated by their ritual of holding hands and exchanging affirmations of love and respect whenever a kernel of conflict arises. Unfortunately, they do not have much time for such private displays of affections when Gerald and Laura arrive – and they will soon sorely need them.

For no sooner have greetings been exchanged than things begin to spin into strangeness. Norm had told Corky that Laura worked as a Vogue editor, but Laura seems nonplused when Corky brings it up. Hmm. Why does Laura claim knowledge of Los Angeles and then refer to the “uptown” neighborhood? (There isn’t one, as Corky points out.) Exactly how long have Laura and Gerald been together? Answers differ. And who sent the gift of three eggplants to Norm and Corky – Laura and Gerald claim no knowledge, despite the Santa Barbara address.

The play slides even deeper into quasi-absurdity when Norm blithely refers to an unfortunate incident in Corky’s own past: that time she had to, um, eat her dead friend when stranded in the Himalayas. Cannibalism: not your traditional icebreaker. (Even Schumer, no stranger to transgressive comedy, hasn’t made that a part of her act, to my knowledge.)

“Meteor Shower” almost seems like several different drafts of a play spliced together, as if Martin wrote a few pages, then rewrote them, but kept all the versions in. The action reels backward more than once, showing us new variations on the scenes we have been watching. Which is the real one? The more pertinent question: Do we much care? For all the glossy appeal of the actors, the play’s shaky tonal shifts, pileup of non sequiturs (Gerald pulling out the works to shoot heroin, for one) and lurches from naturalism to absurdity render it strangely weightless. While the underlying story, we eventually glean, is an oblique examination of the psychic strains of marriage and the mysterious impulses of the subconscious (I think), it’s hard to gain much insight when the play keeps wobbling off its axis.

The actors, to their great credit, keep the mostly aimless proceedings at least watchable. They’re working under the direction of Jerry Zaks, who seems to have just thrown up his hands at the script’s potholes and told everyone to have a good time. Fair enough. Fans of Schumer hoping to see her brash, outsized comic persona on full display may leave feeling a little disgruntled, but she acquits herself honorably in her Broadway debut, proffering a few choice bits of physical comedy – as when Corky lewdly feeds Laura a celery stick with her feet. (Yeah, that happens!) She also proves herself a master at what on film would be called the reaction shot, offering everything from genially blank stares that seem to double the size of her face to hilariously detailed befuddlement as events take ever more bizarre turns.

Key, also making his Broadway debut, has a gleaming stage presence, exuding both slyness and sexual magnetism – key parts of his character’s makeup. Benanti, ravishing in a champagne slip dress, does an amusing parody of the exotic femme fatale, all come-hither eyes and kittenish laughter, with an edge of savagery underneath. Her surface sweetness sours when Laura and Gerald occasionally begin verbally clawing each other’s eyes out, to their hosts’ alarm. Shamos is terrific at playing baffled good guys, and the aptly named Norm is precisely the type, desperation flaring in his eyes as he tries to keep the evening on an even keel, especially when Laura begins making predatory approaches. But then sex seems to be on everyone’s mind, as the innuendos and revelations begin to flow.

“Meteor Shower” – which can be seen as a fantastical variation on “Who’s Afraid of Virginia Woolf?,” with the games mainly being “get the host” rather than “get the guest” – fully explodes into lunacy about midway through when one of the characters is hit by a bit of space debris, with predictably unfortunate results. This would be outlandish enough, but it’s the shrugging reactions of the other characters that shuts down any sort of engagement with these people as people. After a few perfunctory expressions of sorrow or dismay, they continue to chat and flirt – and flirt some more – as if someone had simply knocked over a tray of crudités, despite the smoldering hole in the chaise longue where a human used to be.

Martin, who of course began his career as a standup comic, supplies a smattering of darkly comic lines (and a veritable pu-pu platter of sex jokes) that the actors deliver with plentiful zest. “When I have to choose between regular and low-fat I understand the phrase ‘dark night of the soul,’” Laura cracks. Corky mockingly observes that she wouldn’t want to be a man because she “couldn’t stand all the advantages.” But “Meteor Shower” still feels like a jumble of scenes, jokes and gags that haven’t been properly assembled into a cogent play. The laughs erupt, but there’s little aftereffect, as with meteors streaking across a blank sky. They register briefly, and then they’re gone.

“Meteor Shower” opened at the Booth Theatre on Wednesday, Nov. 29, 2017.

Creative: Written by Steve Martin; Directed by Jerry Zaks; Scenic Design by Beowulf Boritt; Costume Design by Ann Roth; Lighting Design by Natasha Katz; Sound Design by Fitz Patton. 

Producers: Joey Parnes, Sue Wagner, John Johnson, James L. Nederlander, The John Gore Organization, Scott Rudin, Eli Bush, FG Productions, Jamie deRoy, Sally Horchow, Sharon Karmazin, Barbara Manocherian, JABS Theatricals, Ergo Entertainment, Seth A. Goldstein, Elm City Productions, Diana DiMenna, Jay Alix & Una Jackman, Jennifer Manocherian, Cricket Jiranek, Catherine Adler & Marc David Levine and The Shubert Organization; Associate Producer: Jillian Robbins 

Cast: Amy Schumer, Keegan-Michael Key, Laura Benanti, Jeremy Shamos, Kate Reinders, Graham Rowat.