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Patricia Arquette likes to go big. In 2018’s “Escape at Dannemora,” she donned copious prosthetics to play a prison employee who assists in an escape. In “The Act” the following year, she played an eerily doting mother with Munchausen by proxy. And in “Severance,” she’s an unhinged boss who lives a double life, surveilling her employees on and off the clock. The actor earned an Oscar in 2015 for a grounded turn in “Boyhood”; on TV, she lets her hair down.

With “High Desert,” Arquette amps up the volume even further. Unlike those earlier outings on the small screen, the Apple TV+ comedy puts her at the top of the call sheet as Peggy Newman, a drug dealer turned methadone user, frontier-era reenactor and aspiring PI. But Arquette brings a supporting player’s lack of inhibition to the leading role. Others might feel the need to rein themselves in and play the straight woman to anchor a cast of eccentrics. Arquette makes Peggy a chaos tornado in feathered bangs, growling and rasping her way through a series of harebrained schemes. An early scene introduces Peggy hanging from a chandelier with her bloomers out, careening into a bar as part of a dinner theater display. The actor then sustains that momentum for eight consecutive episodes.

The namesake High Desert is a region two hours’ drive and a world away from Los Angeles. From the midcentury Instagram bait of Palm Springs to the Joshua tree-studded Yucca Valley, it’s a deeply strange, profoundly beautiful place — an ideal setting for the register “High Desert” is aiming for, a cross of Coen brothers kookiness and California noir, and one that director Jay Roach makes the most of. Still, a compelling backdrop can’t sustain a show forever. Over time, “High Desert” starts to feel as shambolic and scattered as its protagonist, unraveling until the season abruptly ends with several balls still in the air.

Creators Nancy Fichman, Jennifer Hoppe and Katie Ford populate this landscape with characters who match Arquette’s antic energy. Peggy’s husband, Denny (Matt Dillon), is an ex-con obsessed with opening a qi gong studio; as she tries to sever ties with him, she finds herself increasingly entangled with Guru Bob (Rupert Friend), a former local news anchor who’s rebranded after a public breakdown. Grieving her mother (Bernadette Peters) and in need of a job, Peggy browbeats sad-sack PI Bruce (Brad Garrett) into taking her on as his unpaid associate, though she still fixates on side hustles like a play starring an actress (also Peters) who’s a dead ringer for her deceased parent. The play will be …cathartic, or maybe the next “Hamilton,” or maybe just something to do. This kind of half-logic guides all of Peggy’s decisions and by extension, the plot of “High Desert.”

“High Desert” has the ill fortune of following “Poker Face,” another show about a woman on society’s margins turned unlikely investigator. The timing can’t be helped, but the comparison underlines a crucial difference: Despite its genre, “High Desert” eschews a case of the week, and with it a consistent rhythm that might offset its all-over-the-place feel. (Peggy works occasional jobs like a wife’s suspected infidelity and a disappearance vaguely linked to Guru Bob, though they tend to float in and out of focus.)

The tone is set by Arquette herself, who blusters and grand- stands in a performance bound to polarize. Like the recent “Hello Tomorrow!,” starring Billy Crudup, “High Desert” takes an actor in the ensemble of a more high-profile Apple project and hands them the spotlight, with mixed results. Like Crudup’s used-car-salesman vibe, Arquette’s maximal commitment turns out to work better in small doses. It is possible to have too much of a good thing, and “High Desert” is hardly inclined to practice moderation.

The first three episodes of “High Desert” are now streaming on Apple TV+, with new episodes airing weekly on Wednesdays.