NEW YORK — In the course of figuring out her approach to the story of the Temptations, playwright Dominique Morisseau sat down one day in Los Angeles with Otis Williams, the only surviving original member of the group. Her goal: to get him to spill the beans.

“So I asked Otis, in as nonconfrontational a way as possible,” she recalled, “ ‘Is there a perspective now that you have that you didn’t have before?’ ”

“You mean, regrets?” Williams replied. 

And then, Morisseau remembered, “He stops talking. He gets emotional. And all I can think is, ‘Oh, if I make Otis Williams cry, my parents will never forgive me!’ ”

Cry, Otis, cry! Of such encounters are biographical musicals sometimes made. And if they excavate some nuggets of bona fide candor, then the resulting musical might, just might, have the potential to become more than a greatest-hits hagiography of beloved figures from the recording industry. This more artful mission is the one the creative team had in mind as they put together “Ain’t Too Proud: The Life and Times of the Temptations,” an anthology show built around one of the most influential groups in Motown, not to mention rock-and-roll, history.

After a well-received trial run last year at the Bay Area’s Berkeley Rep, “Ain’t Too Proud” continues its long march toward Broadway with what its producers describe as a crucial month-long visit to the Kennedy Center, with performances starting Tuesday  and an official opening night set for June 28, when reviews will appear. Additional stops are scheduled for Los Angeles and Toronto, as the show both awaits word on a suitable space among the 41 theaters of Broadway, where availability is tight, and takes advantage of the time to make adjustments to the show.

Des McAnuff, who won his first Tony 25 year ago for his direction of “The Who’s Tommy” — one of the first musicals to develop a rock-group album into a stage story — says shaping the music of the Temptations for the theater has been relatively easy. “Happily, the themes that affected their lives are very much alive in the songs they sing,” McAnuff said by phone from Bloomington, Ind., where “Ain’t Too Proud” stopped for several days for technical refinements. “The harmonies and certainly the electrifying music they were generating, and is still with us, have become classics.”

That an assembly line has formed to manufacture popular rock songbooks into jukebox shows doesn’t necessarily mean the road to Broadway success is a breeze. Entries in the genre, such as the Tony-winning “Jersey Boys,” based on Frankie Valli and The Four Seasons; the Abba-inspired “Mamma Mia!”; and “Beautiful: The Carole King Musical” can make theatergoers forget how many others have crashed and burned. Anyone recall “Ring of Fire,” the Johnny Cash musical that lasted a month on Broadway in winter 2006? Or “The Times They Are A-Changin’,” a two-month wonder featuring the songs of Bob Dylan? Or, for that matter, this past season’s flop, “Escape to Margaritaville,” with the songs of Jimmy Buffett and a life span ending July 1, foreshortened by anemic ticket sales?

To stave off the shopworn and infuse the project with as much authenticity as possible, lead producers Tom Hulce and Ira Pittelman, of “Spring Awakening” and “American Idiot,” among others, recruited Morisseau. Her highly praised plays on hot-button issues such as the hardships befalling blue-collar workers (“Skeleton Crew”) and urban education (“Pipeline”) have made her a sought-after voice by theaters across the country. As recounted by Hulce, the actor-turned-producer famous to film fans for his role in “National Lampoon’s Animal House” and starring as Wolfgang Amadeus Mozart in Milos Forman’s Oscar-winning “Amadeus,” he mentioned “two or three names” to an influential acquaintance as to a book writer for the project, “And he said, ‘Dominique Morisseau.’ ” 

Born and raised in Detroit, where she graduated from a high school for gifted and talented students, and went on to the University of Michigan, where she honed her writing skills, Morisseau was steeped in knowledge of the city and the lore of Motown. “The Temptations is my parents’ favorite group,” she said, recalling stories of how the group’s members also grew up there. None of this was lost on the producers: Pittelman had for several years held the option on the rights to the Temptations’ music, and after he and Hulce read her plays, several set in the Motor City, she became their first and only choice.

“There is something about her language that is her own, and connected to Detroit,” Hulce said.

The Temptations’ string of R&B successes is of such a magnitude — “42 top-10 hits and 16 number ones,” said Pittelman — that there could be no problem with audiences being heart-meltingly familiar with the archives. “My Girl,” “Get Ready,” “Ain’t Too Proud to Beg,” “I Could Never Love Another (After Loving You)”, “Just My Imagination” — and, as they say on those late-night commercials, there’s more! The composition of the group, which, by the way, still performs, has changed dramatically over the years since the breakthrough in the mid-1960s; there have been two dozen Temptations who have cycled in and out of the group.

It is Williams’s 2012 memoir “The Temptations” on which the show is based, with a concentration on its storytelling from the mid-’60s to 1974 and some of the group’s earliest members, such as Paul Williams, Mel Franklin, Eddie Kendricks and David Ruffin. (Smokey Robinson, who wrote some of the group’s best-known songs, is a character in the musical, as well.) Morisseau has tried to link their stories to the tumultuous currents of the times, which correspond to the accelerating influence of African American artists on the music industry, as well as to the burgeoning civil rights movement. 

“There is something important about artists and where they stand in a moment of civic unrest,” she said. “It feels like we’re having this contemporary conversation [in the show] about another time.”

As McAnuff notes, the Temptations were pioneers in multiple respects, not the least of these concerning the particularly theatrical style of performance they honed. Modeled on influencers such as the Cadillacs, the Temptations dazzlingly incorporated dance into their act. “The Cadillacs knew about movement and choreography, but the Temptations took that to an entirely new level,” the director said.

This placed a daunting responsibility on choreographer Sergio Trujillo. Although his credits have included “Jersey Boys” — also directed by McAnuff — and another more recent, dance-oriented jukebox show, “On Your Feet!,” the story of Gloria and Emilio Estefan, Trujillo came to “Ain’t Too Proud” feeling he had to prove himself again. “Of all the shows that I have done, this is the one that has the most pressure,” he said, “because these guys were known for their moves.”

Expect to see a lot of those moves onstage in the Eisenhower Theater, and even a few more. It seems that the young actors who have been recruited might be able to out-Temptation the actual Temptations. “The things that I have them doing,” Trujillo said with a laugh, “I don’t know that the real David Ruffin could do.”

Ain’t Too Proud: The Life and Times of the Temptations, book by Dominique Morisseau, music and lyrics from the Motown catalogue. Directed by Des McAnuff and choreographed by Sergio Trujillo. June 19-July 22 at the John F. Kennedy Center for the Performing Arts. or 202-467-4600.