Every year the Christmas season offers a bountiful feast for Twin Cities music lovers. Handel’s “Messiah” can be heard in various styles all over town, while the ageless Doc Severinsen brings “Jingle Bell Doc” to Orchestra Hall, and just down the street, those genre-bending exponents of avant-garde and often whimsical jazz, the inventive trio known the Bad Plus, settle in for their annual residency at the Dakota.

Formed 16 years ago by two musicians raised in Golden Valley, drummer David King and bassist Reid Anderson, and a pianist from Menomonie, Wis., Ethan Iverson, the trio has released 11 studio albums while touring extensively. Following their four nights at the Dakota, they will wrap up the year at the Village Vanguard in New York City.

Their sound is unique. The piano trio, going back to its inception in the late 1930s with the King Cole Trio headed by Nat King Cole, has existed chiefly as a showcase for the pianist. Bass and drums — or guitar and drums in the case of Cole’s group — took an accompanying role, providing rhythmic and harmonic support and an occasional solo.

The Bad Plus alter that formula, bringing democracy to the old format while expanding the boundaries of what is expected of a piano trio. The three voices in the group carry equal weight, both as composers and players. And they cut a wide swath stylistically, from ’70s-style fusion jazz to intimations of bebop to pop and rock deconstructions. They give a nod to various traditions while adding their own quirks and oddities and unresolved harmonic tensions. At times they practice a kind of musical Cubism, as if one were hearing opposite sides of a composition at the same time.

For their first (70-minute) set Thursday, they drew from a wide range of their recorded output, from the subtle and mysterious “Everywhere You Turn” off their 2003 album “These Are the Vistas” to their latest release, “It’s Hard,” an album of covers that includes a rumination on the old Cyndi Lauper hit “Time After Time” and, offered Thursday night as a encore, a wry parody of Johnny Cash’s “I Walk the Line” with echoes of Floyd Cramer-style piano from Iverson.

“Everywhere You Turn” showed off one of their trademarks: a soft, lush tune in the piano propelled by feathery percussion from King that slowly built to a huge crescendo and then faded away at the end.

All three played with fluent virtuosity throughout the set, King and Anderson evolving a furious counterpoint during Ornette Coleman’s “Street Woman” that seemed to surprise and energize them both. A highlight mid-set was a harmonically bold treatment of a Prince song from their latest album, “The Beautiful Ones” from the “Purple Rain” soundtrack.

The Bad Plus, we hope, will be back next Christmas.

Michael Anthony is a Twin Cities critic.