Working in a similar vein is “Jagged Little Pill,” which began life last year at the American Repertory Theater in Massachusetts and arrives in November at the Broadhurst Theater. Featuring a book by the Academy Award-winning scriptwriter Diablo Cody and directed by Diane Paulus , “Pill” weaves songs from Alanis Morissette’s 1995 album of the same title into a portrait of a suburban family riven by topical ills that include opiate addiction, racism and sexual assault.

My colleague Jesse Green, who saw it in Boston, found the show a bit “overwrought.” But, he added, it “takes on the good work we are always asking new musicals to do: the work of singing about real things.” This from a reviewer who has called the jukebox form “the cockroach of Broadway.”

Admittedly, Mr. Green was in that instance referring specifically to a jukebox subgenre, the bio-musical, which uses singers’ chart-toppers to trace the arcs of their careers, the most recent Broadway example being “The Cher Show.” This season brings us “Tina: The Tina Turner Musical,” a hit in London (directed by Phyllida Lloyd of “Mamma Mia!”), where I saw it last summer.

“Tina” dutifully honors the now classic bio-musical outline and its clichés: adversity, success, more adversity, triumph (or collapse) before the final curtain. It is squarely in the tradition of such “Behind the Music”-style Broadway fare as “Jersey Boys” (the Four Seasons musical) and “Beautiful” (the Carole King musical).

But like those shows, its cookie-cutter outlines allow for the possibility of a transcendent star performance, one that pushes past note-by-note impersonation into idiosyncratic portraiture. That was what was delivered by John Lloyd Young , as Frankie Valli in “Jersey Boys”; Jessie Mueller, channeling Ms. King in “Beautiful,” and, last season, Stephanie J. Block as Cher.