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:

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.