Not so long ago, it seemed as though some kind of legislation had been passed decreeing that Broadway musicals could come in only a handful of styles. The musical adapted from a popular movie. The nostalgia-driven show recycling songs from pop charts past. The Disney family spectacle. The pop-opera born of the British invasion in the 1980s, whose legacy held sway despite the failure of many imitators.  But the recent successes of musicals that fit none of the regular molds have changed the game, perhaps for good — and certainly for the betterment of the current Broadway season. Consider the three most recent Tony winners for best musical, the king-making prize that usually all but guarantees financial success and a profit-spinning road tour.  “A Gentleman’s Guide to Love & Murder,” which took home the prize two years ago, was a left-field oddity: a comic operetta with a serial killer as its nominal hero. Last year, the mostly somber “Fun Home,” adapted from Alison Bechdel’s graphic novel about a lesbian’s relationship with her closeted gay father, triumphed over the more traditionally nostalgic and almost equally well-received “An American in Paris.” And this year — yes, I know, I’m going out on a limb here — my usually unreliable crystal ball has been glowing for almost a year now, announcing the anointment of “Hamilton,” the rap-inflected über-smash about one of the lesser-known Founding Fathers, as the big winner.  Anomalies all, but their success seems to have inspired some fresh thinking in the minds of Broadway producers, who, sensibly enough, given the long odds against success, are often tempted to stick to the tried and true, if not the trite and tired. The spring season on Broadway this year features perhaps the most eclectic lineup of new musicals in recent memory, from an antic spoof of bad movies to a gentle fable based on a popular children’s book.  In order of their openings, let me introduce the class of spring ’16, in all its freak-flag glory. That spoof I referred to, bluntly (and bravely!) called “Disaster!,” opens March 7 at the Nederlander Theater. First staged Off Off Broadway more than three years ago, this gleefully over-the-top parody of the brief deluge of disaster movies that flooded movie screens in the 1970s was written by the impish Broadway baby Seth Rudetsky and Jack Plotnick. The musical is set on a floating disco that’s hammered by (a) an earthquake; (b) a subsequent tidal wave that capsizes the vessel; and (c) various other unnatural natural calamities, including a swarm of killer bees and a school of piranhas. Accompanying the mayhem is a host of familiar, often cheesy songs from the era (“Torn Between Two Lovers,” anyone?). For the Broadway version, the production has collected a sensationally savory cast, including the heavenly Kerry Butler (of the similar “Xanadu”), Roger Bart (“The Producers”), Adam Pascal and Faith Prince. If you’re going down with the ship, it’s hard to imagine more blissful company.  “Bright Star,” opening March 31 at the Cort Theater, marks the Broadway debut of Steve Martin. Steve Martin, the composer, that is. Mr. Martin, better known as a comedian, movie star, novelist, art collector — and playwright — is also a great fan of bluegrass music. He wrote the book and composed the folk-flavored songs with Edie Brickell, the onetime platinum-selling singer, who also provided the lyrics. Set in North Carolina in both the 1920s and the 1940s, this unabashedly romantic, highly dramatic (even melodramatic) musical, which I saw in San Diego in 2014, tells the story of the traumatic life of an unmarried young woman who gets pregnant, with complicated consequences.  The antihero of “American Psycho,” opening April 20 at the Gerald Schoenfeld Theater, is, well, a maniac. Based on Bret Easton Ellis’s novel about a young Wall Street hotshot whose hobby is, well, viciously violent murder, it was originally staged in London by Rupert Goold, who remains at the helm here. Duncan Sheik (“Spring Awakening”) provides the score, and the playwright Roberto Aguirre-Sacasa wrote the book.  In a decidedly more delicate hue is the stage version of the Adrienne Shelly movie “Waitress,” opening April 24 at the Brooks Atkinson Theater. This might seem to conform to the standard screen-to-stage formula, except that most previous entries in that crowded field have been based on popular movies. Ms. Shelley’s 2007 indie film is lesser-known, the serio-comic story of a diner hash-slinger stuck in an unhappy marriage. Broadway wattage, however, is supplied by both the star, the superlatively talented Jessie Mueller, a Tony winner for best actress in a musical for “Beautiful,” and the composer-lyricist, Sara Bareilles, who has a large following for her almost unclassifiable brand of richly felt pop songs.  Disney seemed to have cornered the market in family musicals over the past two decades, regularly producing splashy, technically sophisticated stage versions of its popular animated movies (and the occasional original, such as “Aida”). But absent a Disney entry this year, some fearless producers have chosen to offer counterprogramming with “Tuck Everlasting,” opening April 26 at the Broadhurst Theater. This gentle-hued musical, first staged in Atlanta and based on the popular children’s book, tells the story of a yearning young girl’s relationship with a family with a magical secret. Toning down the razzle-dazzly showmanship that made his name in musicals like “The Book of Mormon” and Disney’s “Aladdin,” the director and choreographer Casey Nicholaw brings a gentler touch to the material (Chris Miller and Nathan Tysen wrote the score), with surprisingly successful results.  My crystal ball has not revealed whether future seasons will feature equally diverse lineups, but it can only be a hopeful sign that this year Broadway has looked beyond its usual borders for stories worth singing and dancing about.  See what’s coming to the stage in our dance and classical music spring previews.  An earlier version of this article misstated the given name of the co-writer of the musical “Disaster!” He is Jack Plotnick, not Joey.  A version of this article appears in print on February 21, 2016, on page AR5 of the New York edition with the headline: Left-Field Musicals Take Center Stage. Order Reprints| Today's Paper|Subscribe
Broadway has had some success lately with shows that ignored tired templates. This spring offers worthy additions to that encouraging trend.