At age 82, Broadway director and producer Harold Prince has 21 Tony Awards—more than anyone in the history of the business. Over the past six decades, he's produced hits from "West Side Story" to "Fiddler on the Roof," and directed shows like "Cabaret," "Sweeney Todd: The Demon Barber of Fleet Street" and "The Phantom of the Opera."

His next project: a new musical comedy based on an obscure Austrian novel, set to 19th-century music and opening next month at a tiny theater in southeast London. Mr. Prince is betting that he can bring the show to Broadway.

Hal Prince in his New York office: 'I'm not a retiring sort of fellow.' Beatrice de Gea for the Wall Street Journal

To get there, he may need to compete against revivals of shows that he helped create. The current Broadway revival of "A Little Night Music," which he directed and produced in 1973, is now a top moneymaker. A revival of "Evita," which he directed in New York in 1979, could hit Broadway in two years. And a "Phantom" sequel, "Love Never Dies," though just postponed from this fall, has announced plans to open in New York next spring.

Some theatergoers might be surprised to learn that a producer of the 1954 musical "The Pajama Game" is still opening new shows—a supposition at which Mr. Prince bridles. "Why are you surprised I'm still here?" he says on a recent afternoon in his Rockefeller Center office, amid posters from popular hits and books of avant-garde plays. "I'm not a retiring sort of fellow, and I've got a lot of energy still." Mr. Prince recently started carrying a BlackBerry and has begun sending text messages, mostly to his wife of 47 years, Judy.

The native New Yorker, who generally goes by Hal, is the son of a stockbroker. He has a theater family: Daughter Daisy Prince is a director, and son Charles Prince is a conductor. Mr. Prince, who bears no outward signs of a stroke he suffered in 2008, divides his time among homes in France, Florida and, at the moment, a New York hotel room while his Manhattan residence is being renovated. Late last year, he purchased a six-story townhouse featuring an elevator and a rear wall of glass. Mr. Prince currently has another New York apartment, on Fifth Avenue, on the market, initially listed at $33 million and recently lowered to $29.5 million, according to public records. Mr. Prince declined to comment on his real estate dealings.

An executive familiar with "Phantom" estimates that Mr. Prince has made more than $100 million off that musical, including tours and productions in other cities. "I haven't a clue," Mr. Prince says when asked how much "Phantom" has earned him.

The strategy behind his new show, "Paradise Found," is a contemporary one. London's 163-seat Menier Chocolate Factory, where he's opening the musical, is hot right now. This week, the Chocolate Factory's production of "La Cage aux Folles" joined its hit staging of "A Little Night Music" on Broadway. Mr. Prince is banking on the theater's image as an incubator of smart shows to help fuel a Broadway transfer for "Paradise Found."

"I think what really all we're talking about is buzz," he says of the nearly six-week run.

Mr. Prince has not had a long-running musical on Broadway since his revival of "Show Boat" in 1994, which followed decades of hit collaborations with composers such as Stephen Sondheim and Andrew Lloyd Webber.

"I think he's frustrated by not having had a hit" commercially in recent years, says Jason Robert Brown, who worked with Mr. Prince as the composer and lyricist for "Parade" in 1998-99 and remains a friend. He adds that it's become tougher to make an artistic and commercial success on high-priced Broadway.

Mr. Prince in his office in 1971. Getty Images

Mr. Prince flatly rejects the notion that he's frustrated and says he pursues subjects that engage him artistically even if he suspects the show will not run long, adding that he never deliberately sets out to top the success of "Phantom."

Mr. Prince still checks in on rehearsals of "Phantom," which has been running nonstop in London and New York since the late 1980s. Last year, when a reunion of "Phantom" fans attended the Las Vegas production of the musical in costumes—many in Victorian garb—at least two people came dressed as Mr. Prince, with bald pates and glasses perched atop their brows, the director's longtime signature look (though he's putting the glasses to actual use more often now).

At a time when the music of rock band Green Day is playing on Broadway with "American Idiot," and "Rock of Ages" star (and former "American Idol" contestant) Constantine Maroulis has his caricature hanging at theater eatery Sardi's, a show like "Paradise Found" could be a risky bet.

Based on "The Tale of the 1002nd Night" by Joseph Roth, an Austrian writer who died in 1939, the musical tells the story of a Shah of Persia who, bored by his large harem, sets off with his eunuch in search of excitement in 1870s Vienna. There, he beds a prostitute whom he believes to be an empress. The show is set to music by composer Johann Strauss II, adapted and arranged by Broadway veteran Jonathan Tunick, with lyrics by Ellen Fitzhugh. Charles Prince will be the show's music director, marking the first time that the elder Mr. Prince has worked with his 46-year-old son.

"Paradise Found" will feature 14 actors—scaled down from 50 that the creators originally envisioned for the production—wearing ornate costumes but performing in a reflective black plexiglass set. Mr. Prince wants to keep the London staging of "Paradise Found" under $800,000, and the New York version under $8 million, says Tim Kashani, a theater producer and technology executive who is one of four lead producers on the project. The show will star Mandy Patinkin, who played Che in Mr. Prince's "Evita," along with Shuler Hensley, who played the Monster in Mel Brooks's "Young Frankenstein," and Kate Baldwin, who starred in the recent Broadway revival of "Finian's Rainbow."

Mr. Prince has mentored several generations of Broadway performers, writers and directors, including 32-year-old assistant director Daniel Kutner, who shares an office suite with him. Mr. Prince often phones him, though Mr. Kutner is only a few steps on the other side of the director's office door. When a name escapes Mr. Prince during an interview, he rings Mr. Kutner: "Dan…Dan…What's the name of my favorite writer whose name I've now forgotten?" Mr. Kutner offers the answer (Austrian writer Stefan Zweig).

"My wife says—I keep saying I'm forgetful, and she says, 'You've always forgotten names since the day I met you,' " says Mr. Prince.

Mr. Prince has picked his "Show Boat" choreographer, Susan Stroman—who went on to direct hits like "The Producers"—to co-direct "Paradise Found," which started rehearsals in New York this week. She'll help shoulder the workload, she says, but adds: "This is Hal's baby."

Of the 39 commercial shows with open-ended runs that Mr. Prince has produced or directed on Broadway, 19 played a year or longer. Some notable flops include an ill-fated musical sequel to Henrik Ibsen's "A Doll's House" called "A Doll's Life," in 1982, and the 1981 musical with Mr. Sondheim, "Merrily We Roll Along," about a Broadway composer turned Hollywood movie producer.

Mr. Prince looks at costumes for 'Paradise Found.' Kevin Tachman for The Wall Street Journal

Mr. Prince says he initially planned a minimalist approach for "Merrily," with actors pulling costumes from racks of clothes on a bare stage, but he backed off from the abstract idea. "I didn't have the guts," he says. After it opened, the show ran 16 performances. Mr. Prince cites his refusal to listen to his instincts on this show as one of his great regrets.

Those who have worked with Mr. Prince say he usually doesn't hesitate to stand his ground. Actress Elaine Stritch, whom Mr. Prince cast in "Company" in 1970, says he is a director who likes actors (not always a given) and he knows what he wants from them. "I think he's very much like me—he's emotionally high-strung but handles it," she says. "He's very selfish and very egotistical about his work. When he's right, he's right, and he knows it."

Carol Burnett, who co-authored "Hollywood Arms," a 2002-03 Broadway play about her dysfunctional family, recalls tussling with the director after she included Tweety, her mother's whiskey-drinking parakeet, in the script. Mr. Prince said the bird had to go. After faxing notes back and forth, finally Mr. Prince wrote: "Give it up!" It won't work!" Tweety was cut.

Their work turned unexpectedly personal when Ms. Burnett's daughter Carrie Hamilton, who conceived of the play and co-wrote it, died of cancer. "I knew he expected me to continue," says Ms. Burnett. "He said, 'You just take care of yourself and we'll be in touch.' " She credits her work with Mr. Prince for helping her through that period. "I think it saved my sanity," she says.

The onetime apprentice to legendary producer and director George Abbott (who himself worked until his death at age 107), Mr. Prince is vocal in his criticism of today's Broadway. His pet peeves are musicals with budgets that soar above $10 million, which he says are often cynical attempts to recreate a successful formula rather than chart new creative territory.

In London, Mr. Prince says, there's still an old-fashioned theater community. "The fellow behind the ticket window will say, 'How's the show going? We're looking forward to it,' " Mr. Prince says.

That's not always so in New York, he says. "Rather frequently, I'll walk up to the box office and say, 'Do you have two seats reserved for Prince?' and they'll say, 'What's the name again?' ".

Write to Ellen Gamerman at ellen.gamerman@wsj.com