When Alanis Morissette released Jagged Little Pill in 1995, critics and rock fans complained, with more and less chauvinism, that the album and its singer were too angry, too shrill, too lame, too loud, too immature, too fake. Jagged Little Pill, the new Broadway musical, which superimposes the album’s songs on to an overwrought story of suburban ennui, should be liable to a lot of that same criticism.

But turn that record over. On Broadway, Jagged Little Pill harnesses the hyperemotionalism of its source to shake off the cynicism and formulaic strictures of the typical jukebox musical. Yes, its plot is shaky and contrived, its songs – and there are so, so many of them – histrionic. It seizes on enough hot-button issues – sexual assault, the opioid epidemic, internet addiction, workaholism, misogyny, sex and gender identity, and OK, sure, gun violence, too – to singe the first row. It is, indisputably, too much and that too muchness is what makes it so watchable.

Morissette signed over the rights to the songs with a proviso: the producers couldn’t create a bio musical, her story was her own. Eventually, screenwriter Diablo Cody (Juno, Tully), who is, like Morissette, a Catholic girl who broke at least a little bad, invented a fictional narrative that would fit the songs. Somewhere in Connecticut lives the Healy family: tightly wound mom MJ (Elizabeth Stanley), workaholic dad Steve (Sean Alan Krill), golden boy son Nick (Derek Klena) and mildly rebellious adopted daughter Frankie (Celia Rose Gooding), who is African American and distrustful of MJ’s chirpy, Instagram-filtered ways. MJ has her own problems. (everyone in this show has problems, even the supporting characters.) A car accident has left her with an addiction to pain pills and triggered memories of an earlier sexual trauma.

Elizabeth Stanley and company of Jagged Little Pill. Photograph: Matthew Murphy

The musical never really settles down to a central subject or a main character, but under Diane Paulus’s vigorous, unsubtle direction it happens so fast and for the most part so fluidly (the set by Ricardo Hernández, with video design by Lucy Mackinnon mostly consists of shifting screens) that it hardly matters. Cody’s script is rich in mildly snarky one-liners – “I have this theory that happy families only exist in orange juice commercials and Utah,” “Your mom is iconic! She’s one salad away from a psychotic break.” The acting is largely strong, particularly Stanley’s brittle, wounded MJ and Lauren Patten, who gives a breakout performance as Jo, Frankie’s sometime girlfriend. She does a combustible, wrenching rendition of You Oughta Know that vaults the screaming audience to its collective feet. Some songs, such as No, from Morissette’s 2012 album, feel extremely apropos, while others, such as So Unsexy and Not the Doctor, slot in less gracefully. Ironic is repurposed as a classroom performance poem. One new song, Smiling, seems unnecessary. Another, Predator, is almost uncomfortably apt.

But the musical, you will quickly discover, isn’t about any one song, story or theme. It’s a mood piece and that mood is largely adolescent. That’s not necessarily a bad thing. Adolescence is the last time most of us will feel things so keenly, will want things so badly, will need so desperately to feel seen and understood. It is a musical reaching toward the misunderstood teenager in all of us. Sidi Larbi Cherkaoui’s athletic, angsty choreography exemplifies this best, asking the chorus to dance as though in the thrall of emotions beyond control. (You can wonder what all of these teens are doing writhing in a well-appointed Connecticut living room, but go with it.) The noisy, outsized unruly feelings that sometimes seemed too big for the album fill a Broadway theater just fine. Ironic, don’t you think?