Last night’s Alaïa show at the Guggenheim began with an Instagram exchange. The museum admired a sculptural, spiraling dress from Pieter Mulier’s last show, writing “perfect” in the comments with a heart-eyes emoji; a conversation started and eventually a date was set.

There’s never been a runway show at the iconic Frank Lloyd Wright-designed building. It was a long, full day of fashion in New York, but with Alaïa’s renown, Mulier’s exceptional talent, and the glamour of the VIP guests—Stephanie Seymour, Liv Tyler, Greta Lee, Lewis Hamilton—there was a heightened sense of expectation in the soaring room. With this crowd, that’s typically an only-in-Paris feeling. The moment a late arriving Rihanna took her seat, the klieg lights flipped on and the models began their long walk down the famous spiral.

The museum informed some of Mulier’s silhouettes, among them the fabulous brushed shearling chubbies in ivory and salmon pink that swirled around the torso, and the micro pleated dresses that were iterations of that sculptural feat from January. Here, they were constructed with the kind of engineering used in jewelry making, snapping onto the torso like a bracelet, and ingeniously staying in place.

Equally, this was a showcase of Alaïa’s fascination with American fashion—he was an avid collector—and with Mulier’s study of it. “I looked quite literally to some American designers that we haven’t forgotten in Europe, but that don’t really have the status of what a Dior has or a Chanel has. And for me, they’re as important as them,” he explained.

The bandeaus and “sweatpants” were riffs on Halston’s 1970s jerseys, while Pauline Trigère cued the double-face hooded swing coats and a sweeping cape worn with matching skater minis, one of Alaïa’s most recognizable silhouettes. Charles James, one of Alaïa’s favorite designers, inspired the most direct reference, the sculpted puffer jackets, as well as the least. Cecil Beaton’s 1948 photograph for Vogue of James’s evening gowns was the starting point for the voluminous track suits in palest pastel taffeta. “I thought it was quite beautiful to bring the essence of American fashion to the collection, which is a sense of ease, which is a different kind of luxury than what we know in Europe,” he said.

The models wore gold chain necklaces suspended from earrings that from a distance looked like wired headphones, bringing Alaïa “down” to the street. Only in New York. “I wouldn’t do this show in Paris,” he said. It was a clever touch from a designer who, you get the feeling, thinks of everything.

On Sunday he’ll host a private viewing at the Brant Foundation of never-before-exhibited photographic reproductions of the pictures Andy Warhol took at the 1982 show Alaïa staged at the Palladium nightclub, a fashion legend brought marvelously back to life. Mulier has been named in the endless talk about the open job at Chanel; he’s one of just a few contenders up to the task, but let’s hope he doesn’t rush off. His Alaïa is so good, and he’s having so much fun.