If the Martha’s Vineyard music scene can be said to have a supergroup, it’s the Edbury All-Stars, who play most Thursday nights at the Ritz in Oak Bluffs. Two of the Island’s most popular bandleaders, Johnny Hoy and Mike Benjamin, along with singer and guitarist Willy Mason, bassist Jessie Leaman and drummer Kevin Medeiros, make up the core All-Stars group.

Mr. Hoy, longtime leader of Johnny Hoy and the Bluefish — which play the Ritz on Wednesdays—took over Thursdays about three years ago when blues guitarist Paul Size left the Island.

“He kind of bequeathed it to me,” said Mr. Hoy, who took advantage of the opportunity to put together a versatile, fun-loving jam band of Island musicians. Mr. Medeiros is the drummer in the Bluefish as well as the Edbury All-Stars, Ms. Leaman plays with the Jaywalkers and the Outskirts and Mr. Mason plays rhythm guitar and sings. Lead guitarist Mr. Benjamin, in Mr. Hoy’s words, “is a ringer like Jeremy [Berlin, the Bluefish pianist].

“Mike was the obvious choice,” Mr. Hoy said.

Willy Mason takes his turn at the mic. — Mark Alan Lovewell

This core group expands to include other musicians, such washboard percussionist Vinnie Padalino, who turned up one recent Thursday and played for most of the evening, occasionally setting down his equipment to dance with another Ritz patron.

The same night, Bluefish guitarist and singer Delanie Pickering stopped in for a beer and found herself pulled into the group by Mr. Hoy and Mr. Benjamin, who handed her his red Stratocaster to lead a country blues song while he stood back and listened, smiling.

“It’s a free-floating situation,” Mr. Hoy said. “Sometimes it’s hard to tell where the audience ends and the band begins.”

Mr. Hoy also invites other Island “ringers” to sit in with the Edbury All-Stars, including guitarist Dana Edelman of the Pickpocket Bluegrass Band and the McMahon brothers, Griffin and Sean, “to keep it from getting stagnant,” he said.

On a typical Thursday night, the All-Stars play almost continuously from 8:30 to 11 p.m., though Mr. Medeiros is likely to have started drumming along with the house music earlier.

Blow Johnny, blow. — Mark Alan Lovewell

Band members take turns calling the tunes, starting with Mr. Hoy, who recently started the evening with a customer request they hadn’t had time to fulfill the previous week: Folsom Prison Blues by Johnny Cash.

With his well-known frayed and bluesy voice, his harmonica taking the place of the twangy guitar riff in the original recording, Mr. Hoy and the Edbury All-Stars immediately drew dancing couples to the small strip of floor space between the band and the bar. The good-time music continued with excursions to New Orleans—Fats Domino’s Hello Josephine, the Wild Tchoupitoulas’ Brother John is Gone—and 1960s Jamaica, with Dandy Livingston’s Rudy, A Message to You (later made famous by The Specials).

The Edbury All-Stars also know their way around southern/southwestern R&B, blues and soul, delivering powerful covers of songs like Roy Head and the Traits’ Treat Her Right, Furry Lewis’s Good Morning Judge and Sugar Pie DeSanto and Etta James’s Down in the Basement.

As the hour gets later, the solos get longer, the dancers grow more joyful and the tunes keep coming: Some Kind of Wonderful, Teenage Wedding, Come and Get Your Love.

For Thanksgiving weekend, the Edbury All-Stars play on Friday night instead of their usual Thursday gig. — Mark Alan Lovewell

“Like everything in life, you start to figure out what you can get away with,” said Ms. Leaman, who also performs her slinky song Own Original Sin and sings lead on the Little Richard barn-burner Long Tall Sally, with Mr. Hoy blowing an extravagant solo.

Mr. Hoy, Mr. Benjamin and Mr. Mason also contribute their original songs to the evening, which usually reaches its crescendo with a funk jam like Kool & the Gang’s Jungle Boogie.

“We always do our best to keep the beat going,” Mr. Benjamin said.

During Thanksgiving week, the Edbury All-Stars play the Ritz on Friday, Nov. 29 at 7 p.m., resuming their Thursday schedule in December.