The premise is that all of a child’s favorite fairy-tale princesses — from folklore and Disney alike — live out their days in a metaphysical green room, waiting to be summoned to work by a wizardly Narrator, played by Adam Godley (of the Tony-winning “The Lehman Trilogy,” among other great things. Oh, why, Adam?). Their labors commence (how? where?) whenever a real kid reads their story. Everything is copacetic until the day Cinderella (the mega-appealing Briga Heelan) is gifted by her fairy godmother (Brooke Dillman, channeling Josephine the Plumber from the old Comet commercials) a copy of Betty Friedan’s “The Feminine Mystique.”

Freeing the women — Cinderella, Snow White (Aisha Jackson), Rapunzel (Gabrielle Beckford), Sleeping Beauty (Ashley Chiu), the Little Mermaid (Lauren Zakrin) among them — from their male-identification fixation leads us in and out of a couple dozen Spears numbers. Such well-known Britney songs as “Toxic,” “… Baby One More Time” and “Oops! … I Did It Again” rotate in with several lesser-known titles by Spears, Max Martin and many others.

Linking a millennial superstar to proto-feminist versions of storybook characters is potentially a lucrative idea for Broadway, if not exactly an original one (e.g. the recent Andrew Lloyd Webber disaster “Bad Cinderella,” which did a quick Times Square disappearing act). “Once Upon a One More Time” also seems revved up — with beat-hitting dances by director-choreographers Keone and Mari Madrid — to go toe-to-toe with a much savvier jukebox musical, “& Juliet.” That show, a pop riff on “Romeo and Juliet,” also features Max Martin songs, several from Spears’s repertory.

Some cast members have been switched out for Broadway: Among the newcomers are Godley and the indispensable Jennifer Simard, who assumes the role of Cinderella’s wicked Stepmother. Her portrayal of a glammed-up troublemaker, a snooty fashion plate out of the Miranda Priestly mold, is fun, because Simard in anything is fun.