Andrew Humann and the “American Idiot” ensemble love rock ’n’ roll. (Jeremy Daniel)

When you write a bunch of hit songs, it’s very important to keep finding ways to make money off of them. One such cash factory is the “jukebox musical,” in which an often-vague attempt at a storyline links together existing songs. (“Mamma Mia!,” pulled from the ABBA canon, is an example.) “American Idiot,” at the National Theatre, isn’t quite that: It expands on Green Day’s 2004 rock opera, about friends who must choose between safe lives in the generic suburbs or generic awesomeness in the generic city. While you can’t grapevine down Broadway without passing a musical cobbled together from pop or rock songs, we think there’s room for shows drawn from these artists’ discographies. 

1. Cher
In the year 2350, a woman with the ability to turn back time, accompanied by her koala-cow half-breed pet, travels into her own history to unite a disparate group of gypsies, tramps and thieves. Along the way, she discovers that the most important thing in life is getting a babe and keeping him got.

2. Lil Wayne
A pussycat-loving young man must take his duffel bag and go on a quest for the mystical “swagga,” accompanied by an ever-shifting group of friends. On their way, he discovers an electric woman whom he must turn on; he ultimately finds success when he learns to stunt like his daddy.

3. Madonna
Born on the small La Isla Bonita, a virgin leaves behind her preaching papa, learns to open her heart and lands a spot on the cover of Vogue. She moves to Argentina, where everyone is crying, but thanks to a nationwide holiday and a lucky star, everyone learns to cherish music like it’s a prayer.

4. Beyonce
Three young women who want a man who can both pay his bills, bills, bills and say their names look to survive, a task made easier because they live in a girl-run world. One gets drunk on the mysterious potion “love,” which makes her go crazy. She’s saved by a magical ring that gets put on it, but always vows to remain an independent woman.

 National Theatre, 1321 Pennsylvania Ave. NW; through Feb. 23, $48-$153; 202-628-6161, (Metro Center)