The cast during a performance of “Some Like It Hot.” Matthew Murphy/Polk & Co. via AP

NEW YORK — “Some Like It Hot,” a Broadway musical adaptation of the cross-dressing movie comedy that starred Tony Curtis and Jack Lemmon, waltzed away Tuesday with a leading 13 Tony Award nominations, putting the spotlight on a show that is a sweet, full-hearted embrace of trans rights.

With songs by Marc Shaiman and Scott Wittman and starring Christian Borle and J. Harrison Ghee, who all got nominations, the show follows two musician friends who disguise themselves as women and join an all-girl band to flee Chicago after witnessing a mob hit. Like the movie, there are men in dresses trying to pass as women. But this time, the dress awakens something in Ghee’s character, akin to a transformation from a caterpillar to a butterfly.

The message of self-acceptance and respect for all was echoed across Broadway, from a revival of “Parade” to a Black actor-led “Death of a Salesman” to the new play “Ain’t No Mo.’”

“I think the pandemic put a lot of things in perspective, both in terms of improvements we needed to make in the community and also just the way that everybody’s feeling about the world and about being a human,” said Ben Platt, nominated for “Parade.” “The art people are making has a real urgency and a real purpose.”

Three shows tied with nine nominations each: “& Juliet,” which reimagines “Romeo and Juliet” and adds some of the biggest pop hits of the past few decades, “New York, New York,” which combined two generations of Broadway royalty in John Kander and Lin-Manuel Miranda, and “Shucked,” a surprise lightweight musical comedy studded with corn puns. The critical musical darling “Kimberly Akimbo,” with Victoria Clark playing a teen who ages four times faster than the average human, rounds out the best musical category.

In the best new play category, nods were distributed to Tom Stoppard’s “Leopoldstadt,” which explores Jewish identity with an intergenerational story, and “Fat Ham,” James Ijames’ Pulitzer Prize-winning adaptation of Shakespeare’s “Hamlet” set at a Black family’s barbecue in the modern South.

The rest of the category is made up of “Ain’t No Mo,’” the short-lived but critical applauded work by playwright and actor Jordan E. Cooper, Stephen Adly Guirgis’ Pulitzer Prize-winning play “Between Riverside and Crazy” and “Cost of Living,” parallel stories of two caretakers and their respective patients.

“Ain’t No Mo,’” which earned six nominations, begins with the United States government emailing every Black citizen with the offer of a free plane ticket to Africa, and each scene explores how various personalities respond to the offer.

Blake DeLong, left, and Wendell Pierce during a performance of Arthur Miller’s “Death of a Salesman” in New York. Joan Marcus/DKC/O&M via AP

Cooper learned he’s been nominated twice – as best playwright and as lead actor – while visiting his childhood home in Texas. He and his family were in the living room where as a 6-year-old, he put on his first plays.

“It is a little bittersweet,” Cooper said. “We only got a chance to do about like 60 performances and this cast and this creative team were like some of the most talented you’ve ever seen. It was unfortunate that people don’t get a chance to experience it because we really felt like it was something special. Audiences felt like it was something special. And it’s just so beautiful to know that the work that we put in – that blood, that sweat and tears – are not in vain.”

“Parade,” a doomed musical love story set against the real backdrop of a murder and lynching in Georgia in pre-World War I, earned six nods, including for Platt, hoping to win a second Tony after his triumph in 2017 with “Dear Evan Hansen,” and rising star and first-time nominee Micaela Diamond.

Wendell Pierce, who has won a Tony for producing “Clybourne Park,” earned his first nomination as an actor on Broadway for a blistering revival of “Death of a Salesman” and Jessica Chastain, an Oscar-winner for “The Eyes of Tammy Faye,” got her first Tony nomination for a stripped down version of “A Doll’s House.”

Pierce will face-off against both stars of Suzan-Lori Parks’ “Topdog/Underdog” – Yahya Abdul-Mateen II and Corey Hawkins – as well as former “Will & Grace” star Sean Hayes from “Good Night, Oscar,” and Stephen McKinley Henderson, who earned his second nomination, having gotten one in 2019 for “Fences.”

Jodie Comer, the three-time Emmy nominated star of “Killing Eve” earned a nomination in her Broadway debut – although her play, “Prima Facie,” did get a best new play nod – and Audra McDonald, who has won six Tony Awards can extend her reign if she beats Comer as best leading actress in a play for “Ohio State Murders.” The last slot in the category went to Jessica Hecht, staring in the play “Summer, 1976.”

Another show that closed quickly nevertheless picked up nominations – “KPOP,” which put Korean pop music on Broadway for the first time. “KPOP” got three – including best original score.

Kevin Woo, center, and the cast during a performance of “KPOP,” opening Nov. 27 at the Circle in the Square Theatre in New York. Matthew Murphy/O+M/DKC via AP

Andrew Lloyd Webber’s frothy and widely panned “Bad Cinderella” earned zero nods, as did “A Beautiful Noise, The Neil Diamond Musical,” a stage biography of the singer-songwriter who has had dozens of top-40 hits. But Samuel L. Jackson earned his first Tony nod for “August Wilson’s The Piano Lesson.”

Two well-received revivals from the late Stephen Sondheim – “Sweeney Todd” with Annaleigh Ashford and Josh Groban, and a star-studded “Into the Woods,” were recognized. “Sweeney Todd” received eight nominations including for Groban and Ashford, and “Into the Woods” earned six, including for Brian d’Arcy James and Grammy Award-winning Sara Bareilles, her third Tony nomination.

“Almost Famous,” the stage adaptation of Cameron Crowe’s autobiographical coming-of-age story, earned just one nomination – for music by Tom Kitt and lyrics by Crowe and Kitt. And choreographer Jennifer Weber had two reasons to smile Tuesday: Weber earned nominations for “& Juliet” and “KPOP,” her first Broadway shows.

Ariana DeBose will host the June 11 awards celebration from New York City’s United Palace theater live on CBS and on Paramount+. It is her second-straight stint as host.