The new musical Billy Baloo has quickly become a hit for the Martha’s Vineyard Playhouse, which is adding five more performances Oct. 23 through Oct. 28.

“It’s totally been selling out, pretty much from the first preview,” said playhouse executive and artistic director MJ Bruder Munafo, who directs the spirited Western dramedy starring Island singers Willy Mason and Lexie Roth.

“One of the most exciting things is that there have been so many wonderful young people coming,” Ms. Bruder Munafo added.

Set in the Rocky Mountains of Colorado in the late 1800s, the gold-rush tale is filled with appealing songs by Mr. Mason’s mother, Jemima James, and his late father Michael Mason, who died early this year after writing the play for over half a century.

Brother Sam Mason, a filmmaker in New York city, rounds out the family production with animated projections that add dimension, movement and intrigue to the action on stage. The set design is by Mac Young.

The live music includes both an overture and an entr’acte, played by an all-Islander trio of musical director and pianist Bill Peek ­— an experienced folk musician better known as a church organist and choir director at the First Congregational Church in West Tisbury — Eric Johnson on bass and Georgie Gude on harmonica.

Willy Mason, who also adapted his father’s book and contributed some of his own music to the show, plays the indolent Billy Baloo opposite Ms. Roth as Ada, the resolute new proprietor of a mining camp’s sole store.

Like Mr. Mason, Ms. Roth grew up in a musical family — her father is acclaimed session guitarist Arlen Roth, a seasonal Aquinnah resident — and went on to her own performing and recording career. The two singers also have recorded together.

Onstage, their characters quickly fall into an easy rapport as Billy tells Ada about the beavers that once lived in the mountains around the play’s setting of Solderville.

Their dams transformed now-shallow Humbug Creek into a stairway of navigable ponds, he sings — “stairs up the steep sides of Creation, chawed by the jaws of the Beaver Nation” — before the fur-hat craze drove Solderville’s beavers to remoter peaks.

Ada, seeking an easier way to haul groceries up the mountain to her store and seeing that the fur trade has moved on, beseeches her new friend to find the four-legged critters and bring them back.

“Come on, Billy, be a believer: All it takes is a couple of beavers,” she sings, rallying him to a folkloric quest that results in some unexpected consequences.

With beavers and ponds restored, the general store flourishes, to the delight of the three bachelor prospectors who’ve made up most of Solderville’s population to date.

Islander Paul Munafo (the director’s husband), film and stage actor Jonathan Lipnick and musician Phil Lee form a hilarious trio as the long-isolated miners.

They also get some of the show’s best songs: Rocks, a witty celebration of the geological processes that brought them all together, and Oysters and Pâté, an ode to the tinned glories of the Perfection General Store that draws extra glamor from Sam Mason’s overhead projection of a rotating oyster shell.

The discovery of silver in Solderville brings a rush of miners, compellingly evoked in projected footage and personified by Islander Ty McDonald as Kevin Kelly, a young man who quickly becomes disillusioned with the mining corporation and admires the independent gold prospectors.

Kevin’s also bedazzled by Laura Lindsay, a saloon-singing ingenue played by New York-based film and television actor Jessie Pinnick, whose sweetly powerful voice soars on numbers like I Got Gold and her winsome duet with Ms. Roth, Beaver Moon.

Mr. McDonald’s standout song is the fiery Speak, Silent Stones, a call for solidarity among the silver workers.

“There’s a fact you must face for the whole human race, that’s that each soul was born as a miner, with an equal share claim registered in his name, and there’s none that deserves any finer,” he sings.

But so big-hearted is this show that no villain ever makes an appearance, even as the melodrama reaches its peak and gunfire rings out.

The corrupt mining corporation remains offstage, while the railroad that threatens to ruin Billy and Ada’s mountain shipping company is represented by a pair of bridges in Sam Mason’s flowing Humbug Creek projection.

An unexpected and highly satisfying denouement restores the balance of nature and commerce to Solderville, where Billy and Ada duet on Ms. James’s enigmatic title song to close the show.

After this week’s performances on Thursday and Friday, Billy Baloo returns next Tuesday through its new closing night on Oct. 28.

All shows start at 7 p.m., with a running time of less than two hours including intermission. For tickets: mvplayhouse.org.