The problem with most jukebox musicals isn’t the juke, it’s the box. The tunes are fine, but they rarely match the container that someone is trying to jam them into. How could they? Commercial pop and musical theater have different kinds of tales to tell and different tools for telling them.

So it’s easy to imagine all the ways “Jagged Little Pill” could have gone wrong. Based on material from Alanis Morissette’s 1995 megahit album and several of its follow-ups, it could have wound up in a bio-musical straitjacket or with a story either too light for the songs’ furious intelligence or too broad for Broadway.

When I saw “Jagged Little Pill” last year at the American Repertory Theater in Cambridge, Mass., I worried that it was falling into the “too broad” category. The script by the “Juno” screenwriter Diablo Cody deliberately aimed to incorporate as many pressing concerns as it could. Rape culture, racism, addiction, adoption, homophobia, global warming, overparenting and underparenting were but a few of the themes dramatized, or at least put (sometimes literally) on placards.

Fair enough: We want certain musicals to do serious work. But in the show’s first incarnation it was often difficult to discern the central story in a plot so over-tangled with issues that it came to seem like a cantata of discontent.