Farce, particularly of the bedroom variety, has traditionally leaned male. A prototypical situation involves a playboy type trying to keep two women apart on a puzzle-box set conveniently equipped with multiple doors.

“POTUS: Or, Behind Every Great Dumbass Are Seven Women Trying to Keep Him Alive,” Selina Fillinger’s comedy that had a turn in the Broadway spotlight in 2022, is a decidedly female addition to the genre. The first word spoken in the play — shrieked, in fact — is an unprintable expletive for female genitalia favored by the Brits.

Fillinger isn’t just being naughty. She’s staking out territory for her side, issuing a theatrical corrective and delivering a feminist proclamation.

An all-female cast of seven makes its own statement.

The characters of “POTUS” are all connected to the unseen occupant of the Oval Office — another randy male president routinely distracted by the consequences of his misbehavior. His team of enablers is fighting a losing battle to make him look good.

The spin room operates on a 24/7 schedule. It’s a pressure cooker, and Harriet (Shannon Cochran), the commanding White House chief of staff, has the weary look of a military general overwhelmed by enemy fire.

More often than not, Jean (Celeste Den), the White House press secretary, is on the receiving end of Harriet’s bellowing commands. Harriet knows she can trust Jean to get the job done, whereas she has less faith in Stephanie (Lauren Blumenfeld), the president’s high-strung secretary, whose main task is blockading his office door when a dalliance is in session.

Margaret (Alexandra Billings), the fed-up first lady, seems to be only adding fuel to the public relations fire. An overachiever with a resume to dwarf her husband’s, she can’t understand why she’s not president — or rather, she has grown tired of accepting the sexist reason.

Meanwhile, Chris (Ito Aghayere), a political reporter on the hunt for embarrassing scoops, has her ear cocked for scandal, which doesn’t take long to arrive. Dusty (Jane Levy), the president’s mistress, saunters in with an announcement: She’s pregnant.

But that’s not the only controversy. Bernadette (Deirdre Lovejoy), the president’s sister, has wheedled her way out of prison. Wearing an ankle monitor and lugging a duffle bag of narcotics, she has come for a presidential pardon but is more likely to be rearrested.

How can Harriet and Jean possibly keep up with the mayhem? Out of this chaos, Fillinger whips up another emergency. The first act culminates with a bust of suffragist Alice Paul flying into the president’s office like a guided missile.

This inadvertent attack on the commander in chief overwhelms even the hypercompetent damage control of this experienced White House team. But never underestimate a group of scared women who have formed an unholy alliance.

Sounds like a laugh riot, no? I wish I could report that the Geffen Playhouse production lives up to its delirious premise, but this spinning top of a play makes itself dizzy from overexertion. Farcical success depends on timing. Flat-footed contrivances, compounded by hackneyed humor and stereotypical targets, contribute to the sense that the play is always a beat behind.

The game cast members, under the direction of Jennifer Chambers, hurl themselves into their roles, fully committing themselves to even the playwright’s most questionable choices. But the strain begins to show.

On Broadway, an ensemble that included Vanessa Williams, Lea DeLaria, Rachel Dratch and Julie White may have distracted from its playwriting problems. But no such luck here.

Stephanie, the president’s Nervous Nellie secretary, undergoes a personality change after dipping into Bernadette’s bag of pills. For a good portion of the second act, Blumenfeld runs around the stage in a swimming tube acting kooky. The bit quickly wears out its welcome, but she gives it her all.

As Dusty is called upon to deploy her sexual talents to divert the president’s secret service agents, Levy delivers lines that are meant to play up the liberation of her character. Her performance as an erotically confident farm girl who slurps blue slushies is vivaciously, at times even scene-stealing-ly charming. But the comedy is too often at Dusty’s expense, and not even her increasing empowerment can compensate for the way she’s demeaned for cheap laughs.

It’s refreshing to see bodily truth liberated from shame, but Chris, the White House reporter who recently gave birth, is defined less by her dogged journalism than by the lactating stains on her blouse. As for Bernadette, there’s not much Lovejoy can do with the gruff, felonious lesbian deployed by Fillinger more as a comic device than a dimensional figure.

Billings, an actor who became a crucial character on the Amazon series “Transparent,” portrays the powerfully contentious first lady role with broad strokes. Punchlines strut from Billings’ mouth as though they’re walking the red carpet at the Academy Awards.

Proximity to realism is reserved for Cochran’s Harriet and Den’s Jean, both of whom do their best not only to right the White House ship but to rescue the play from its worst excesses. It’s a losing game when drugs and violence inflame the increasingly preposterous action.

The cast is up against not only an out-of-control plot but a set by Brett J. Banakis that is as logistically cumbersome as the play’s subtitle. Stagehands are set in frantic motion when a different corridor of the White House is required or the scene shifts to the ladies’ room.

At least “POTUS” has the courage of its zany conviction. It’s a thrilling sight to see a stage full of women unleash their power for the benefit of womankind rather than a single, over-promoted man. The play transforms in the end to a feminist rally, but too many false farcical moves spoil the emancipatory fun.