The cult documentary “Grey Gardens” is hardly a natural candidate for musicalization. No tuner has ever been adapted from a doc, much less a plotless one about a wildly eccentric mother-daughter pair — Big Edie and Little Edie Beale, relations of Jackie O — living in co-dependent squalor with a lot of cats.

But the unconventional show, with music by Scott Frankel, lyrics by Michael Korie and book by Doug Wright (“I Am My Own Wife”), is just the latest in a long line of unorthodox musicals that originated at Off Broadway’s Playwrights Horizons.

And it has even proved a hit for the org: The show’s sold-out run, which began Feb. 10, has extended through April 23, as far as the theater’s sked will allow.

The nonprofit’s name makes it easy to forget that it doesn’t just develop the work and career of playwrights. It also supports composers, lyricists and librettists.

“Gardens,” after all, follows in the footsteps of such unique musicals as Shaun Davey and Richard Nelson’s adaptation of “James Joyce’s The Dead,” which transferred from Playwrights to Broadway in 2000, and William Finn’s legendary “Falsettos” trilogy, the first of which, “In Trousers,” was the theater’s first stab at a tuner in 1979.

“Playwrights has such a specific history in terms of developing new musicals,” Frankel says. “Something that’s outside the mainstream vernacular seems to be their meat and potatoes.”

Frankel and Korie, in making their New York debut at the theater, join a long list of tuner creators — including Finn, currently repped on Broadway with “The 25th Annual Putnam County Spelling Bee” — whose careers were kick-started at Playwrights. Lynn Ahrens and Stephen Flaherty (“Ragtime”) debuted “Lucky Stiff” (1988) and “Once on This Island” (1990) there; Adam Guettel (“The Light in the Piazza”) launched “Floyd Collins” in 1996; and Jeanine Tesori (“Thoroughly Modern Millie,” “Caroline, or Change”) debuted “Violet” in 1997.

Also produced by Playwrights: two important preems from Stephen Sondheim himself, “Sunday in the Park With George” in 1984 and “Assassins” in 1991.

Of course, other nonprofits regularly develop new tuners, including Lincoln Center Theater (headed by former Playwrights a.d. Andre Bishop), the Public and the Vineyard.

But unlike Lincoln Center and the Public, whose missions have broader scopes that incorporate revivals and international writers, Playwrights’ sole mandate is the presentation of new work by American scribes.

And the 35-year-old theater, with an annual operating budget of $8 million and two intimate auditoriums (one of 198 seats and one of 99-128), is a smaller-scale operation than LCT or the Public.

“Because of our size, there’s a perception that our work can be more adventurous,” says Tim Sanford, who has been a.d. at Playwrights since 1996.

“The stakes are a little bit lower at Playwrights Horizons than at Lincoln Center,” says Ira Weitzman, who played a pivotal role in developing new tuners at Playwrights and now serves as associate producer for musical theater at LCT.

It was Weitzman and Bishop who changed the charter of Playwrights in the late 1970s to include new American musicals.

“We were really the only theater in the city, and maybe the country, seriously developing new writers of musical theater,” says Bishop. “Very few, if any, were taking that on yet.”

Over the years, the theater has managed to build a modest but loyal subscriber base of about 5,000 members hungry for challenging new work.

“It’s the nature of the audience that defines the work at Playwrights,” says James Lapine, the writer-helmer whose musical work with the org includes two installments of the “Falsettos” trilogy and “Sunday in the Park.” (His latest play, “Fran’s Bed,” opened the current season there.) “They have a devoted subscribership that’s not as reviewer-driven.”

Such a following has helped Playwrights cultivate an atmosphere that’s less risk-averse than a more commercial environment.

“The tradition is not just to take a chance on new writers, but to welcome them back even after they fail,” says Ahrens.

Adds Flaherty: “Everything doesn’t rise and fall on any one project. That’s not the way to encourage fresh writing.”

Sanford also makes it a point to nurture the theater’s artists as a community. “A lot of musical theater alumni will just show up,” Wright says of the development process. “You have people like Bill Finn and James Lapine popping in for a reading or catching a preview.”

But for all the rewards that go along with the theater’s commitment to developing new tuners, the large-scale commercial success of a Broadway mega-hit isn’t usually one of them.

“That’s not really the point,” Sanford says.

Take “Grey Gardens.” The tuner, which cost $900,000 to produce, won across-the-board raves for star Christine Ebersole and is doing big B.O.

But a Broadway transfer won’t happen. “We couldn’t afford to, even if we sold out with no ads,” Sanford says.

And maybe bypassing the Rialto suits a work as eccentric as “Gardens.”

“Where I imagine there may be a life is a kind of consortium of regional theaters presenting a sort of mini-tour,” says ICM agent Patrick Herold, who represents Frankel, helmer Michael Greif and several other members of the creative team. A similar mini-tour was done with “Floyd Collins,” which was remounted in San Diego, Philadelphia and Chi three years after the 1996 Playwrights premiere.

And high on Sanford’s to-do list is an original cast recording of “Grey Gardens.” A CD is invaluable in helping a new musical carve out an ongoing place for itself, and can fuel future productions the way the recording of “The Spitfire Grill,” presented by Playwrights in 2001, helped spur multiple stagings of the tuner all over the country.

“Once a show’s part of the canon,” Sanford says, “our job is done.”