The Turtle Island String Quartet, which performed Sunday at the Maine Center for the Arts in Orono, is the crossover group of all crossover groups.

When this eclectic foursome was founded in 1986, the classically trained players not only swung between classical and jazz forms, they invited all the kids on the musical block to join the party. Rock, hip-hop, bluegrass, funk and world music turned up in their arrangements and compositions.

So it makes perfect sense that violinists David Balakrishnan and Evan Price, violist Danny Seidenberg and cellist Mark Summer gamely showed up Sunday with four-time Grammy Award-winning Cuban clarinetist Paquito D’Rivera. Not only does D’Rivera share the Turtles’ enthusiasm for genial improvisational outbursts, but he appreciates the way they hover somewhere between Haydn and Count

Basie, between Mozart and Frank Zappa.

More to the point, the Turtles – and, one assumes, this is true of any featured guests lucky enough to tag along with them – represent outright playfulness with imagination, the fruitful and fun exploration of unthinkable combinations. It’s as if they filter a score through a prism and come up with something beautifully bent. That means a performance of “Cool,” from Leonard Bernstein’s “West Side Story” has a chunky groove going on. Or “The Girl from Pathetique” weaves that old “Ipanema” tune into Tchaikovsky, and the result is strange, amusing and, of course, rigorous.

D’Rivera joined the troupe for about half the program and added a steamy sexiness to the rhythm of the evening. On this tour, he has pushed the quartet into yet another crossing: this time to clarinet quintet, an inspiration of Mozart’s. D’Rivera’s luscious melody “Danzon,” based on a Cuban national dance, was, at heart, an homage to Mozart.

The audience favorites, however, were sultry collages of old tunes, such as “Angel Eyes” (think Frank Sinatra and Nelson Riddle doing mambo), “You’ve Changed” (ever heard cha-cha-cha on a violin?) and “A Night in Tunisia” (with unexpected hip swivels by D’Rivera).

The Latin-influenced chamber music works were, perhaps, most interesting to the classical music crowd. D’Rivera introduced “La Jicotea,” a melting-pot piece the Turtles commissioned him to write. It contains his Cuban roots, as well as elements of classical and jazz music, and accentuates the quirky performance styles of the musicians, who sometimes play their string instruments as if they were guitars and drums (and that doesn’t even give due credit to the wah-wah pedal on the cello).

Admiring the achievements and elasticity of the Turtle Island String Quartet, or quintet if you include D’Rivera, is easy. The group goes for laughs, amiability and a firm sense of mission. For some, the aesthetic may have brief appeal, as in: A little of this stuff goes a long way. But this is a group that has proved its place in the bastion of 20th century cleverness, talent and nonconformity.