CHICAGO — The conductor sat cross-legged on the floor, but this was not a rehearsal break. Instead, Doug Peck, the music director and orchestrator for the Goodman Theater production of “The Jungle Book,” was leading an 11-piece band through a sinuous show tune while pumping a harmonium from the center of a large Persian rug.

Arrayed around him, also seated in traditional Indian style, were players on sitar, vina, tabla and Carnatic violin. To his left, a jazz sextet sat on chairs with music stands.

As the band rolled through the familiar Dixieland rumble of “I Wanna Be Like You” and the sunny swing of “The Bare Necessities,” sax and sitar traded improvised solos, and tabla and drums found fresh grooves together. Richard M. Sherman, a songwriter on the 1967 animated film, looked on approvingly, tinkering with lyrics, chiming in with musical advice, or singing along when the occasion moved him.

This exuberant jam session between Indian and jazz musicians riffing on a trunk full of old Disney tunes comes courtesy of the local theatrical auteur Mary Zimmerman. This isn’t the first time that Disney Theatrical Group has entrusted a beloved animated musical to a visionary director — a MacArthur “genius” grantee to boot — whose big idea is to take aesthetic inspiration from the story’s far-flung location, in this case India. That could also describe the winning gamble Disney took in 1997 with Julie Taymor and the African elements she added to her stage version of “The Lion King.”