It’s not just the art of Jean-Michel Basquiat that his family curates in “King Pleasure,” an exhibition on now at the Grand in Los Angeles. It is also his life itself. “King Pleasure” was put together by Basquiat’s sisters, Lisane and Jeanine, together with his stepmother, Nora Fitzpatrick, and the Basquiat specialist Dieter Buchhart. The show supplies a vast, coherent, and immersive overview of Basquiat’s work. It also represents the boldest attempt yet to re-frame his personal narrative—principally, but not entirely, by what it omits.

Three of us who know the facts of Basquiat’s early life—Al Diaz, Danny Kessler, and myself—regrouped recently to debrief the show, which we had each seen during its New York run. We met Jean at City-as-School, which was, and is, an “alternative” public high school, then based in Brooklyn, now in Lower Manhattan. At C.A.S., teachers were “advisers” who sometimes taught, but also guided students through the experiential-learning emphasis of the program. Danny is now a sociology professor; Al, who was Jean’s partner in the famous SAMO graffiti project, works full-time on his art.

For creative mavericks, C.A.S. provided the most nurturing environment imaginable, but Jean still had a troubled career there. It culminated, or perhaps bottomed out, when he pelted principal Frederick Koury with a cream pie at the 1978 spring graduation ceremony. (This happened after Jean had been dismissed from the school, not before—one of many factual inversions promulgated by Jean himself.) While Jean was there, however, C.A.S.’s emphasis on the five boroughs as campus provided him with the opportunity to hone his protean adaptability—high life and low, erudite to common denominator. Jean developed the ability to integrate and ingratiate himself everywhere.

The boldest attempt yet to re-frame Jean-Michel Basquiat’s personal narrative—principally, but not entirely, by what it omits.

He was sexually as well as socially protean, and his bisexuality—perhaps the word is “pansexuality”—has been, at most, glancingly discussed in biographical material. But Jean was both bisexual and extremely promiscuous at C.A.S. His sexuality was a major, if perhaps underlying, catalyst for the hostilities between him and his father, Gerard Basquiat. Gerard was paradoxical, as his daughters acknowledge in the catalogue accompanying “King Pleasure.” The background they supply there is instructive, whereas their recollections as videotaped for the exhibition are mostly boosterism.

Gerard sometimes invited Danny to play tennis, and the time spent alone with Gerard gave Danny a sense of his complexity. One minute Gerard would be discussing the rarefied poetry of Stéphane Mallarmé; in the next, he’d crudely refer to his son as a “pussy faggot bitch.” Al, Danny, and I—as well as many others—certainly believed Jean’s claim that his father was physically abusive. Jean displayed his bruises, and his fear of his father was palpable. Jean’s mother, Mathilde, was institutionalized, and, according to Danny, “a source of endless pain.” Jean blamed his father for his mother’s condition. He loved his sisters and worried about them.

“King Pleasure” takes us all the way back to Jean’s infancy, through home movies and artifacts from the family’s archive. As his chronology advances, included are samples of the Basement Blues Press—the C.A.S. student newspaper on which Jean, Al, and I worked. Jean’s art back then was curvilinear and hippie-ish, a world apart from the scabrous imagery that blistered his adult canvases. And yet his interest in the word was manifest always: wordplay, word tags, word imagery, word signifiers, are a through line.

In my 1977 C.A.S. yearbook, Jean signed a cryptic message that punned on the “last daze” of the school term. A shining sun rose out of his written inscription. Jean always imagined words and images as a kind of synesthesia in which each translated and transmuted the other.

Jean’s sexuality was a major, if perhaps underlying, catalyst for the hostilities between him and his father.

Among the exhibition’s highlights are spectacular life-size installations re-creating his Great Jones Street studio, in Manhattan’s NoHo, and the Mike Todd Room, in the former Palladium club on 14th Street, for which he was commissioned to contribute canvases. He hung out there, too, which added to the lure of the club itself. These rooms are imprinted with his invisible presence.

Jean’s overdose death, in 1988, left a large body of work that nevertheless was irrevocably finite—thus allowing new fortunes to be made. As indeed they have been. His work solicits astronomical auction bids; his museum exposure is vast, and so is the commercial licensing that stamps his imagery on sneakers, T-shirts, backpacks. Adjacent to “King Pleasure” is a large gift shop crammed with merchandise.

Ultimately, “King Pleasure” provokes more questions than it answers—about art, commerce, the making of myth and narrative, the contours of family, the evolution of sensibility. It is not the final word, but it does demand that the spectator provide his or her own transcription. If pleasure was indeed king in Basquiat’s life and work, pain was its ubiquitous consort.

“Jean-Michel Basquiat: King Pleasure” is on at the Grand in Los Angeles through October 15

Joel Lobenthal is a historian and cultural critic who has written books on subjects ranging from Tallulah Bankhead to Yuri Soloviev, Patricia Wilde, and 60s fashion