You know you’ve really arrived when you have multiple shows running in New York simultaneously. It’s fair to say that Sam Shepard, John Patrick Shanley, and Shakespeare have all made their presence felt this season. But is puppeteer Basil Twist giving them a run for their money?

Over at Dodger Stages, Mr. Twist’s famous underwater creation “Symphonie Fantastique” tickles the senses with banners that rush through the water-filled tank that is his stage. But refusing to rest on his (damp) laurels, this past weekend at the Japan Society, he opened “Dogugaeshi,” his ode to the sliding door.

Mr. Twist explores a style of sliding panel set-design rarely used today (he was inspired by a snatch of old documentary film on Japanese puppets). When the dogugaeshi technique first appeared in the 17th century, it served a pragmatic function. Scenes painted on panels parted to show more panels, which then parted themselves, ad infinitum. This allowed a puppeteer to create endless rooms in deep perspective, with diminishing shoji screens seeming to retreat into the distance. It soon became its own attraction, turning into a kind of splashy finale after a show, with dozens of screens parting in rapid succession.

On the island of Awaji, there are still a few theaters employing the method, but only as a curiosity – the same way sliding flats are preserved at Drottningholm. A commission from the Japan Society allowed Mr. Twist to spend time learning about the style and interview those who had seen it in its heyday. Now, he uses the ancient technique together with his own figural puppetry and a healthy dose of video projection. The result is a haunting, abstract piece about lost traditions.

In Mr. Twist’s set, painted chrysanthemums part onto fighting tigers, which flip around to show geometric patterns. It’s like the wood-and-paint version of multimedia, with images giving way to one another in surprising ways. And then Mr. Twist adds real multimedia – he and Peter Flaherty project interviews, images of whirlpools, and a chasing sequence of tall red gates that the audience seems to fly through. This is the second time this season that Mr. Flaherty has had to evoke a brightly lit Japan (he worked on Complicite’s “The Elephant Vanishes”), and he does so with elegance and restraint.

The gliding quality of the projections contrasts with the bumpy, halting progress of Mr. Twist’s wooden screens. Sometimes the screens whip around, or vanish perfectly off stage, but last Thursday they occasionally put up a bit of a fight. Even when a screen refused to budge, however, it simply underscored the astonishing difficulty of the task at hand. A fox spirit, a handheld, feathery white puppet darting mischievously around the screens, all reminded us of the unpredictability of the medium. If the screens had moved silently on ball bearings, they could never have seemed so alive.

Mr. Twist’s “Symphonie” has a cohesive, sweeping effect, largely because of the Berlioz that underscores it. Here, he collaborates with Yumiko Tanaka, a noted composer and performer on the shamisen. Seated on a platform that rotates in and out of view, Ms. Tanaka appears playing a different instrument almost every time you see her. Unlike the Berlioz, her accompaniment has a cooler, less narrative, thrust. She sets the tone for the experience: an amused, meditative calm. With “Dogugaeshi,” Mr. Twist makes something both small and spectacular – and he opens a door on an enviable tradition.

Until November 23 (333 E. 47th Street, between First and Second Avenues, 212-752-3015).