Director Will Davis has a brief list of bullet points he likes to scroll through when deciding if a theater production is the right fit for him. At the top of that list is a particularly crucial question: “Is there something on the page that’s proposed in this play that is impossible for the play to do?”

“If the answer is yes,” he says, “then I definitely am interested.”

That’s why he decided to direct the Shakespeare Theatre Company’s production of “Everybody,” a reimagining of the 15th-century morality play “Everyman.” In playwright Branden Jacobs-Jenkins’s version, which was a finalist for the Pulitzer Prize in 2018, the character of Everybody ends up on death’s doorstep. As Everybody marches toward the afterlife, the character crosses paths with people who personify various concepts, including Friendship, Beauty, Strength and Stuff.

The idea that Everybody could be any of us is driven home by the play’s high-concept conceit: Five actors are in contention to play the title role each performance at the Lansburgh Theatre. A live, onstage lottery determines which one will take on the lead, with the other four actors taking supporting roles. For actors Alina Collins Maldonado, Avi Roque, Kelli Simpkins, Ayana Workman and Elan Zafir, that means they not only must know all 10 roles that they could be called on to play, but they also must be prepared to embody those parts at a moment’s notice.

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“When you have a stress dream about the theater, it’s basically what this play is proposing: that you’re going to show up and you don’t know who you’re supposed to be,” Davis says.

The meta-theatrical production builds on a common task faced by actors cast as understudies (or swings), who typically are asked to learn multiple roles and step in when a cast member is absent. But “Everybody” embeds that unpredictability into the show on a daily basis, presenting audiences with 120 potential casting combinations.

“I was very intrigued and excited and scared by the idea that, as the actor, you come every day and you don’t know who you’re going to play,” Workman says. “It’s my worst fear to be, like, ‘I have to learn all of these lines and just say yes and be present.’ But it’s also such an amazing, exciting opportunity as an actor to challenge yourself that way.”

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That challenge manifested itself in a rehearsal schedule that largely threw convention out the window. Understanding that it was not plausible to fine-tune all of the different casting permutations, Davis regularly allowed the lottery to determine the roles in rehearsal. He also frequently asked actors to flip roles from moment to moment, in a technique he affectionately refers to as the “swippy-swappy.”

The fluctuating rehearsal process emphasized how a sequence could play out differently depending on the scene partners, as they’re drawn from a diverse cast of actors, each of whom brings a distinct personality to the production.

“If I’m talking to them,” Zafir says, gesturing to Roque, “or I’m talking to her” — meaning Workman — “it’s like a different play.”

The odds of the lottery producing the same configuration of actors and roles at three or more of this run’s 37 performances is less than 1 percent. Although the lottery may initially read as a gimmick, “Everybody’s” casting serves the play’s universally accessible themes of self-reflection and mortality.

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“Life is random,” Roque says, “and the timeline around when you leave this Earth also possesses some unpredictability.”

The cast members have found the play to be as freeing as it is daunting. In a world in which actors are selected — or rejected — for roles in part because of such traits as gender, race and sexuality, “Everybody” allows its performers to essentially play a part they rarely, if ever, get to tackle onstage: themselves.

“Honestly, I did not understand the play,” Maldonado says, about her initial reaction to the script. “What I did understand was that I didn’t have to fit a box. It was moment of, ‘This would be such a relief to just be me.’ ”

Correction: An earlier version of this story misspelled the last name of playwright Branden Jacobs-Jenkins. This version has been updated.

If you go

Everybody

Shakespeare Theatre Company’s Lansburgh Theatre, 450 Seventh St. NW. shakespearetheatre.org.

Dates: Through Nov. 17.

Prices: $35-$120.

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