Pippa Pearthree and Patrick D. Kennedy in ‘The Addams Family.’ (Jeremy Daniel/The Kennedy Center)

It used to be audiences knew the names of the people who wrote the shows: Irving Berlin, Cole Porter, Rodgers and Hammerstein, Andrew Lloyd Webber.

Nowadays, the musicals that aren’t ripping off jukebox hits often ride the high tide of big pop titles: “The Lion King,” “Spider-Man,” “Mary Poppins,” “Shrek,” “Sister Act.” Who knows composers?

That makes “The Addams Family” an interesting case as it arrives at the Kennedy Center’s Opera House this week. The $16 million musical is plainly spinning forward the franchise of appealingly subversive Charles Addams cartoons that seemed foolproof in TV and movie versions. It got mixed reviews in Chicago and was bashed in New York, despite marquee stars Nathan Lane and Bebe Neuwirth as the mordant Gomez and Morticia. (Douglas Sills and Sara Gettelfinger have the roles now.) Remarkably, the show has been significantly rewritten prior to this tour.

Of course there is a composer in the middle of this: Andrew Lippa. And at 47, he is perhaps beginning to emerge with full force, and not just with “Addams Family,” even though the affable Lippa calls it his biggest show to date “in all measurable ways.”

First, the saga of the franchise rewrite:

Composer Andrew Lippa. (Courtesy of Creative Artists Agency/Creative Artists Agency)

A Broadway musical of “The Addams Family” was the brainchild of producer Stuart Oken, a former executive vice president at Disney Theatrical. Long an “Addams” fan, Oken says his thinking was guided by the marriage of the cartoon “Lion King” with then-downtown director Julie Taymor, “where something unexpected yet fundamentally mainstream could come out.”

By the time the show began its pre-Broadway tryout in Chicago, the mesh was off. Marshall Brickman and Rick Elice (“Jersey Boys”) were writing the book. Lippa was writing music and lyrics. Design and direction were by Phelim McDermott and Julian Crouch, the British duo whose wicked “Shockheaded Peter” (which they described as a “junk opera” done with the trio the Tiger Lillies) was among the projects earning international notice.

As the show moved to Chicago, Broadway veteran director Jerry Zaks was brought in. Oken is diplomatic about what went wrong, but he invokes the famous phrase that “musicals are written; they’re rewritten.” And the more the team kept trying to hammer the material into shape for the Chicago premiere, Oken says, the more “chemistry started to evade us.”

The mixed reviews and gossipy reports from Chicago “sent shock waves out into the world that something was wrong,” he adds. “And it was. But it wasn’t SO wrong.”

A lot of the trouble boiled down to a rewrite that nobody could figure out before New York, where the critics were tough. The plot originally focused on Wednesday, the splendidly gloomy girl who scandalizes the spooky family with her desire to date a “normal” boy. Gomez and Morticia, the creative team soon realized, didn’t have enough to do. And those were the characters people most wanted to see.

“We kept thinking we were solving it,” Oken says. “But we didn’t solve it.”

“Addams” sold reasonably anyway, even if it ended up only recouping 70 percent of its investment after two years on Broadway. (Oken says the touring versions — it’s already running abroad, with more productions to come — will eventually recoup the whole investment.) And the group thought the work could still be better.

The show got a moderate do-over involving a plot change, the cutting of four songs and the addition of three. Elice says the producers bankrolled a full five weeks of rehearsal, not the usual two for a tour, plus two weeks to tech the show into its first national touring venue in New Orleans.

“That came with a real price tag,” Elice says.

Of Lippa’s role, Elice points out that changes to the score are the most complicated in any show, requiring work with everyone from the book writers to orchestrator and musical director and performers. “And Andrew,” says Elice, “in a rather amazing way, said, ‘Let’s do it.’ ”

Lippa is still best known for his 2000 breakout show “The Wild Party,” though thanks to one of the strangest twists in musical theater history, he doesn’t even get that moment entirely to himself. Just as Lippa’s “Wild Party,” with Idina Menzel, Taye Diggs, Brian D’Arcy James and Julia Murney, was being produced at the off-Broadway Manhattan Theatre Club, Michael John LaChiusa’s “The Wild Party” was being staged on Broadway with Mandy Patinkin, Toni Collette and Eartha Kitt.

The slow evolution into his own solid professional identity may be part of why Lippa says of himself, “I was an impatient, angry young man. Now I’m a patient, angry middle-aged man.”

Lippa, who sounds genial enough, didn’t even see himself as a full-fledged musical theater composer until around 2006, when friends and colleagues urged him to focus on his own work. He cobbled together all kinds of work around his own writing projects, including music directing for Kristin Chenoweth’s concerts. (Chenoweth’s 1999 Tony Award, let it be noted, came for her turn as Sally in “You’re a Good Man, Charlie Brown,” with several new songs by Lippa — including Sally’s “My New Philosophy.”)

The guidance to just write “was a good bit of advice,” says Lippa, who was born in Leeds, England and raised in Michigan. “It focused me, helped me push the projects faster.”

The projects are beginning to come quickly indeed. In the pipeline:

●“A Little Princess,” based on the 1905 Frances Hodgson Burnett children’s novel. A concept CD was released last fall, featuring Sierra Boggess (Broadway’s “Little Mermaid”) and Laura Benanti. The licensing process for productions has just begun.

●“The Man in the Ceiling,” based on the Jules Feiffer book. Like “Princess,” it’s been in the works for some time; it was developed by Disney, then languished and now is scheduled for a reading in January.

●A commission about Harvey Milk for the San Francisco Gay Men’s Chorus, which will feature 300 voices. The piece will debut next June, with more cities already lined up to perform the non-narrative piece that Lippa calls, for lack of a better word, a “fantasia.”

●“Big Fish,” a big musical to be directed and choreographed by Susan Stroman (“The Producers,” “The Scottsboro Boys”). Based on the Daniel Wallace novel that became a 2003 Tim Burton film, the show is scheduled for Broadway next year. Oken already says, “I’m sure it’s Andrew’s best work.”

●An untitled original musical to be written with the inexhaustible John Logan (the play “Red,” the upcoming James Bond picture, and the recent screen adaptation of “Sweeney Todd”).

Lippa’s musical hallmarks? Oken likes the “emotion, humor and melody.” Lippa credits influences as diverse as Motown and everything on 1970s pop radio to Leonard Bernstein for his explorations in classical, jazz and Broadway forms. Elice describes Lippa’s music as “very catholic in its breadth. It has great heart and great wit, in that order.”

There is a bigger picture for Lippa, who has been with his partner David Bloch for 14 years (they married in 2008): He is studying to become an Interfaith minister.

“I wasn’t being of service,” Lippa explains, adding that one of the things he loves about the theater is its pluralism. “Everyone is welcomed,” he says. “And I want to take part in a spiritual life that does the same.”

He’s on track to be ordained as soon as next June, which is why the current joke around his house, he says, goes like this: “Music and lyrics by the Reverend Andrew Lippa.”

The Addams Family

Book by Marshall Brickman and Rick Elice; music and lyrics by Andrew Lippa. Directed and designed by Phelim McDermott and Julian Crouch, with creative consultation by Jerry Zaks. At the Kennedy Center Opera House, July 10-29. For information, call 202-467-4600 or visit kennedy-center.org.