As you approach Lincoln Center, a large metal frame fills the plaza, around which rise three of the center’s stately theatres, homes to ballet, opera, and symphonic music. Above the familiar fountain hangs a ten-foot disco ball. This is the Dance Floor, the centerpiece of Lincoln Center’s festival, now in its third year.

The initiative, which fills the gap left by the much lamented Lincoln Center Festival and Mostly Mozart Festival, is of the little-bit-of-everything variety. As Shanta Thake, the center’s chief artistic officer, said recently, “we believe that more is better.” Accordingly, includes almost nightly dance parties on the plaza, along with film screenings, poetry readings, civically minded discussions, augmented-reality experiences, musical performances, and more, spread across the complex’s open and indoor spaces.

The vast majority of events are free; select indoor performances are pay-what-you-wish. In place of the weeks-long Mostly Mozart Festival, the newly named led by the incoming music director Jonathon Heyward, offers seven programs (July 20-Aug. 10), at David Geffen Hall.

These contain everything from works by Haydn and Mendelssohn—and some Mozart!—to “City of Floating Sounds,” a tech-driven, interactive symphony by Huang Ruo. Performers in “Avimukta,” Ashwini Ramaswamy and Aparna Ramaswamy (left to right). And there is dance—and not just the participatory kind that goes on under the disco ball.

As part of “India Week” (July .