For jukebox musicals with a fictional plot, one common approach is to center the plot around one or more (fictional) singers or musicians, thus letting some of the songs be performed as songs within the show. Examples of such musicals include Boogie Nights (1998), Mamma Mia!
Jukebox musicals with fictional stories frequently center on a few (imaginary) singers or musicians, using their music to tell the story.  Examples like "Boogie Nights" (1998) and "Mamma Mia!" demonstrate this approach.