No, Kate doesn’t get spanked. And for those wondering how the dicey ending of “Kiss Me, Kate” — that musical mashup of “The Taming of the Shrew” and backstage battling exes — would come across in these more sensitive times, well, that’s also been reconsidered for the Roundabout Theatre Company’s Broadway revival of the Cole Porter musical, with “additional material” by composer-lyricist Amanda Green.

The clever navigation of this Golden Age musical through today’s waters of gender politics is one of several plusses in an otherwise uneven production that is still able to score some highs in terrific dancing, Kelli O’Hara’s performance and, oh, those Porter songs.

Though the original production opened six years after “Oklahoma!,” four after “Carousel” and the same season as “South Pacific,” the news that a show could integrate character, story and themes into a musical whole seemed to have made little impression on Porter and on book writers Bella and Sam Spewack. As for making the script remotely credible, it was still anything goes. But with Porter’s hit-packed score, who cared?

Director Scott Ellis’ production doesn’t try to make much sense of a narrative that includes Damon Runyon-style gangsters in a far-fetched subplot, and instead sticks with a playful spirit in the hopes that audiences will ride out the nonsense as long as the show delivers on entertainment. And it often does, especially when it dances to Warren Carlyle’s choreography, whether it’s in the frisky “Tom, Dick or Harry” or in the sizzling Act 2 opener “Too Darn Hot,” featuring Corbin Bleu and James T. Lane in impressive solo turns.

Of course, making sport of egomaniacal, narcissistic and hyper-theatrical actors is a sure thing. (See also: “The Prom.”) Here ham is served with a side of humanity, so the over-the-top exuberance is tamped down.

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