Billy Bigelow hits Julie Jordan. Henry Higgins molds Eliza Doolittle. Fred tames Lilli. And Edward rescues Vivian.

Amid a national reckoning with sexual harassment and misconduct, Broadway is mounting a cluster of musicals this season and next that, some theatergoers already contend, romanticize problematic relationships between women and men.

The titles are beloved: “Carousel,” “My Fair Lady” and “Kiss Me, Kate” are classics of the canon, while “Pretty Woman,” a new musical, is adapted from a smash film. And each of their female protagonists has her own strength — strength that in some cases changes the men in their lives.

But elements of the stories — and the fact that all four productions are being directed and choreographed by men — are prompting new scrutiny at this #MeToo moment.