Had Rupert Holmes’s career ended in the early ’80s, he would be most widely remembered for “(Escape) The Piña Colada Song,” a lovably hokey pop single that was his biggest hit as a singer/songwriter. In 1985, though, Mr. Holmes made a splash in the theater world as composer, lyricist, and librettist of “The Mystery of Edwin Drood,” a music hall-inspired adaptation of an unfinished Charles Dickens novel that, famously, allowed each audience to vote to determine its outcome.

For his latest outing, Mr. Holmes — whose more recent efforts include “Curtains,” a collaboration with the renowned musical team of composer John Kander and lyricist Fred Ebb — has turned to Gilbert and Sullivan for inspiration. The result, “Pirates! The Penzance Musical,” is as frothy as a piña colada, and as rollicking in spirit as “Drood,” albeit not quite as cleverly drawn as the latter.

The premise is keen enough: Take “The Pirates of Penzance,” a long-beloved comic operetta introduced during the Victorian era, and transport it to New Orleans, tweaking the setting, story, and musical arrangements to accommodate one of our country’s most storied cities and, most significantly, the birthplace of jazz. 

Director Scott Ellis, whose many Broadway credits range from effervescent musicals, among them “Curtains” and a revival of “Drood,” to classic plays, has recruited a sterling cast for the undertaking. I can’t think of an actor better suited to deliver “I Am the Very Model of a Modern Major-General” than David Hyde Pierce, and the stage and screen veteran does not disappoint, infusing the verbose classic with his signature deadpan drollery.      

In addition to playing the puffed-up but adorable Major-General Stanley, who gets mixed up with a crew of pirates when they pursue his daughters, Mr. Pierce turns up briefly as librettist William S. Gilbert himself, introducing “Pirates!” in a winking prologue that also features an amusing Preston Truman Boyd — later cast as a breathless police sergeant — as composer Arthur Sullivan.

Tunes from a few of that duo’s other shows, including “HMS Pinafore” and “The Mikado,” are sprinkled in as we follow Frederic, a young apprentice to the pirates, as he tries to pursue his own path, which includes courting the lovely Mabel, one of Stanley’s daughters. Nicholas Barasch’s Frederic is an appealing male ingénue, bringing boyish vigor and a limpid tenor to the part, while Samantha Williams’s sassy Mabel adds spice, as do the lively performers cast as her siblings.  

It’s also fun to watch Ramin Karimloo, a dashing leading man known for his work in brooding mega-musicals such as “The Phantom of the Opera” and “Les Misérables,” further flex the comedic muscles he showed off in a recent revival of “Funny Girl” as the Pirate King — a part last played on Broadway by Kevin Kline, whose flair for physical comedy is evoked here. Jinkx Monsoon, a two-time winner of “RuPaul’s Drag Race,” mugs effectively as Ruth, Frederic’s devoted nanny.

Still, Mr. Holmes’s new book can suggest a protracted skit that, over two acts, starts to lose its punch. His musical adaptations, which benefit from vivacious orchestrations by music director Joseph Joubert and Daryl Waters, tend to be more intriguing: “Climbing Over Rocky Mountain,” for instance, has been re-imagined as the swinging “We’re Sashayin’ Through the Old French Quarter,” while “Poor Wand’ring One,” Mabel’s coloratura showcase, is brought down to earth, in notes and in flavor, acquiring a more languid, sultrier quality.

For “The Nightmare Song,” from “Iolanthe,” Mr. Holmes and his collaborators channel a jazz funeral, with choreographer Warren Carlyle engaging ensemble members in a dream ballet that incorporates sprightly tap dancing. David Rockwell’s scrumptious set is similarly evocative, summoning the romance of a New Orleans plaza and a sense of whimsy suited to the motley characters.

Mr. Holmes’s revised ending, a re-fashioning of “He is an Englishman” from “Pinafore,” titled “We’re All From Someplace Else,” seems designed to make a political statement, albeit gently and cheekily. Mostly, though, “Pirates!” is content to be the very model of a modern musical trifle, and if you don’t mind lavishing two hours and change on such an offering, it has its charms.