Disney's “Aladdin,” on tour at the Kennedy Center — one of four shows on Broadway now directed by Casey Nicholaw. (Deen van Meer)

Director/choreographer Casey Nicholaw currently has four musicals running on Broadway: “Aladdin,” “The Book of Mormon,” “Mean Girls” and “The Prom.” It’s the first time anyone’s done that since 2016, when Nicholaw had “Tuck Everlasting,” “Something Rotten,” “Aladdin” and “The Book of Mormon” running simultaneously. Before that, you have to go back to 2001, when director Susan Stroman did it.

Nicholaw is the reigning king of the Broadway musical, and his touring edition of “Aladdin” is now at the Kennedy Center. Though the story about a poor young boy, a princess and a genie in a lamp has been around for centuries, this version is explicitly based on the animated Disney movie, the box-office champ of 1992. The challenge for Nicholaw was to translate that cinematic experience into a distinctively theatrical one.

“You’re not going to have Aladdin and Jasmine fleeing a volcano with lava flowing everywhere onstage,” he says over the phone from his lake house in New Jersey, “because it will look lame if you try. So we had to shift the emphasis from the visual effects to the singing and dancing, from an adventure story to a classic Broadway musical comedy. We got rid of the animals and added more songs. We didn’t have to cut dialogue, because we were going to have to expand from a 90-minute movie to a 150-minute musical anyway.”

A highlight of the original film was the Genie, voiced by Robin Williams, singing “Friend Like Me.” As he improvised new lyrics for the song, he did impressions of everyone from a snooty French waiter to a barber and a boxer, from Cab Calloway to Ed Sullivan, and the animators were able to change the Genie’s body into each new shape instantly. Obviously, that would be impossible to replicate onstage.

Disney's “Aladdin,” on tour at the Kennedy Center. (Deen van Meer)

“We decided to get as far away from Robin Williams as we could,” Nicholaw says, “because people start comparing, and no one wants to be compared to Robin. We hired James Iglehart, who is a stand-up comedian and very funny in his own right, as our first Genie, and the character is built from his interpretation. We can’t shape-shift onstage, so instead we change channels in the number: from a ‘Dancing with the Stars’ thing to a ‘Let’s Make a Deal’ game show, a tap number, a club act, some Bollywood, some ballroom, some magic tricks and more.”

It helped that Alan Menken, the show’s composer, was on hand for the first rehearsals and could explain that his and lyricist Howard Ashman’s first concept for the show was closer to a Broadway musical than the Hollywood movie it became. So Nicholaw went back to the show’s origins, restored four songs cut from the original script and added four songs written by Menken and book writer Chad Beguelin. The additional songs allowed Nicholaw to expand the role of dancing in the storytelling.

“You have to tell a story that’s good and then figure out where you can enhance it with song and dance,” Nicholaw argues. “When Aladdin sings ‘Proud of Your Boy,’ for example, you learn more about him, how he feels like an underdog, how he’s trying to win the approval of his mother, than you could from just the dialogue. And I always remind myself that what I’m doing is musical comedy, so I want the dances to be buoyant and funny. I don’t want it to seem like the comedy stops and then the dancing begins.”

Casey Nicholaw, director-choreographer of Disney's “Aladdin” (on tour at the Kennedy Center), “Mean Girls,” “Book of Mormon” and “The Prom.” (Deen van Meer)

The director grew up in San Diego, where he couldn’t quite fit in with the jocks or the straight-A kids. But when some friends suggested that he join the San Diego Junior Theatre, the city’s nonprofit company for young performers, he was cast in “Annie Get Your Gun” and was immediately hooked. “I loved the sense of community,” he recalls, “and the theater’s back-and-forth energy that you don’t get from a movie.”

During the spring break of his freshman year studying theater at UCLA, he went to New York and did some auditions just as a lark. He landed a job doing summer stock in New London, N.H., earning $150 for 10 shows. “I was 19,” he says, “and it was the best summer of my life.” When the season ended, he moved to New York City with his new friends and started performing wherever he could. After a lot of non-Equity jobs, he landed a role in “Crazy for You,” the 1992 Broadway adaptation of George Gershwin’s “Girl Crazy.”

“For seven of the eight shows I did on Broadway,” he notes, “I was in the original companies, so I got to see how they were put together, and I was fascinated by the process. After that, I always felt I watched musicals with a director’s eye, but I never had a chance to do it. So I hired a rehearsal studio, created three big dance numbers from scratch and invited all the directors and producers to come see them. From that I got a job offer to choreograph a new musical version of ‘The Prince and the Pauper.’”

Soon after that, director Mike Nichols hired him as the choreographer for “Monty Python’s Spamalot,” which earned him an invitation to direct and choreograph “The Drowsy Chaperone” in 2007. He’s been busy on Broadway ever since. This week he hosts the first readings for a new musical adaptation of the 1959 Marilyn Monroe movie “Some Like It Hot,” featuring new songs by Marc Shaiman and Scott Wittman, the same team that did “Hairspray.” He hopes it will arrive on Broadway in a couple of years.

“I never set out to have four musicals on Broadway at the same time,” he admits. “I feel like I’m always working, but you never know when you’re going to get a theater, and how the timing’s going to work out. I’m just lucky that ‘Aladdin’ and ‘The Book of Mormon’ have run for so long.”