OVER THE COURSE OF MORE THAN 20 BOOKS, Percival Everett has produced as rich a body of fiction as just about any contemporary American writer, but mainstream literary recognition has proved elusive. As an African-American writer deeply interested in the American West, and one with an experimentalist bent, he’s certainly no marketer’s dream. His books range so freely — from satire to absurdism, from realism to metafiction — that it’s difficult to get a fix on him. Then again, the same might be said of Cervantes, Sterne, or Twain.

Identity is the bedrock of the rational. Aristotle’s theory of identity holds that each entity has a specific nature. An owl cannot be a monkey; an elevator cannot be a marimba. Destabilize identity and the ground beneath our feet crumbles: We risk falling into madness. It’s no accident that Everett’s two variations on Greek myth, For Her Dark Skin (1990) and Frenzy (1997), bring readers inside the minds of Medea and Dionysus, those avatars of the irrational. Indeed, so thoroughly do his books complicate identity and undermine logic — in terms of both content and form — that they elude critical categories.

Everett’s new book, Assumption, begins as a standard crime novel, though anyone familiar with the author will know it’s unlikely to stay that way. The protagonist, Ogden Walker, a deputy sheriff in remote Plata, New Mexico, likes his job well enough, even if he’s not especially good at it. He’s bothered by the imagined disapproval of his dead father, a black man who didn’t care for police and generally despised white people even though he married one. Ogden’s mother lives nearby and is the only person outside of work who Ogden sees regularly. The narrator remarks, “It was hard for a son to think that his father hated half of him,” underscoring the internal split, or doubling, that becomes clearer as the narrative unfolds. Ogden “deeply love[s]” the New Mexican landscape yet feels “like a failure remaining there,” sensing there was “a life he was not pursuing.” Like many of Everett’s protagonists, Ogden comes to us burdened by the past, by others’ expectations, by accumulated disappointment and stress, and by an ever-sharpening sense of mortality.

Death figures in an abstract prologue that vividly conveys the Western terrain:

He thought about the desert around him, thought about water and no water, the death that came with too much water, flooding that carried mice and snakes and nests and anything else in its way. To drown in the desert, that was the way to die, sinuses replete with sandy water, dead gaze to dead gaze with rattlers in the flow.

 The crimes Ogden investigates — murders, missing persons, drugs, hate groups — take him to Albuquerque, Dallas, Denver...