A great Broadway moment: a big ensemble singing “Another Op’nin’, Another Show,” and the curtain rises, and off they go, as Roundabout Theatre Company’s revival of the beloved musical Kiss Me, Kate opens at Studio 54.

The song tells us to “frame your mind/ To mirth and merriment,/ Which bars a thousand harms and lengthens life.” Good advice from Shakespeare in The Taming of the Shrew, that gender-vexing comedy that gave Cole Porter the basis of his musical comedy.

The source of the show’s “mirth and merriment” — which may not lengthen your life all that much — is a play within a play. The Shakespearean lead roles — Katherine, the shrew, and Petruchio, the shrew tamer — are being played by Lilli Vanessi and Fred Graham, who used to be married to each other and are now ferociously flirting and fighting, daring old passions to reawaken, so the backstage battles mirror the onstage battles. There are preposterous subplots involving Lilli’s current suitor (who is the commander of the U.S. Army), a gambling debt, and two gangsters who fall in love with the theater, not unlike the current TV show Barry. Their vaudeville duet, “Brush Up Your Shakespeare,” should be more hilarious than it is.

Kelli O’Hara plays Lilli/Kate, and her glorious soprano is well-matched with Will Chase’s splendid baritone. The trouble is that O’Hara’s stage presence always exudes elegance and a kind of kindness, not the wildcat spitfire Kate is supposed to be. The second couple, Lois Lane (understudy Christine Cornish Smith stepped in to deliver “Always True to You in My Fashion”) and Bill Calhoun (the terrific Corbin Bleu, who leads the ensemble scenes like “Too Darn Hot”). Warren Carlyle’s choreography is high-energy, but Paul Gemignani’s music direction is too high-volume, sometimes obscuring Cole Porter’s witty lyrics. And the distance between Porter’s ironically winking songs and this production’s comic mugging is an issue thoughout.

Insider joke: The warfare between Lilli and Fred is ignited by a misdirected bunch of flowers, “pansies, rosemary and violets, my wedding bouquet.” Edward Albee, in Who’s Afraid of Virginia Woolf, has that famously battling couple parody that moment when Martha says, “pansies, rosemary and violence, my weddin’ bouquet.”

Shakespeare’s obnoxious conclusion has Kate, tamed by sleep- and food-deprivation, advise women to obey their men, and she offers her hand for her husband to step on. In the double-wedding conclusion of KMK, she offers her hand, not to be stepped on but to be taken. In some excess of hashtag awareness, director Scott Ellis has Petruchio kneel and lay his head in her proffered hand. Taming-reversal doesn’t really solve the human or the dramatic problem.

Theater

Kiss Me, Kate

Roundabout Theatre Company. Through June 30 at Studio 54, 254 W. 54th Street, New York.