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MILAN — Founded here in 1913 as a luggage purveyor to the local carriage trade, Fratelli Prada probably would not have become a synonym for Italian fashion had the male scion, uninterested in the business, not passed it on to his daughter, Luisa, who in turn eventually handed the baton to a daughter of her own, a girl named Miuccia.

By 1978 Miuccia Prada was running the family company and barely six years later had altered the course of both her family’s fortunes and the history of fashion by introducing a line of bags — a backpack was the key item — in an industrial nylon previously used as lining material.

Turning things inside out is a characteristic element of Ms. Prada’s disposition. As if in allusion to that fact, her show this week was held in a warehouse adjoining the Prada Foundation, on the southern outskirts of the city. The warehouse may or may not be the actual depot for designer’s world-class collection of contemporary art. And while is certainly conceivable that the stacks of crates stenciled with “This Side Up” arrows and the Prada name rendered backward contained untold millions worth of contemporary art, they might just as easily have been empty.

Keeping people guessing is one of Ms. Prada’s fallback strategies. Particularly in a conservative city and in an industry that prizes continuity over innovation, it is useful to have a voice as contrarian as hers. While many designers in Milan are busy chasing the romanticized Neo-Edwardian hothouse vision that has made Alessandro Michele’s Gucci such a staggering success, Ms. Prada chose instead to revisit her own chastely industrial back pages with a show that recast her 1980s pocone nylon bags as clothes: vests, jackets, long coats, trousers, shorts, all in voluminous upholstery proportions.

Certain of the items were created in collaboration with architects or designers like Herzog & de Meuron; her longtime collaborator Rem Koolhaas; Konstantin Grcic, and the French brothers Ronan and Erwan Bouroullec. (Mostly they produced bags — a “frontpack” from Mr. Koolhaas — that suggested the wisdom of holding on to one’s day job.) These eventually gave way to logo sports and work wear reminiscent of the things that the brand produced during the period when Ms. Prada’s husband, Patrizio Bertelli, sponsored a boat, the Luna Rossa, that came close to winning the America’s Cup.

Backstage at Prada men’s, fall 2018.CreditValerio Mezzanotti for The New York Times

It was a sedate show, a decidedly commercial one. And yet even within framework of her own design conventions (afterward Ms. Prada said, as though reading from a Monty Python script, that she “could not get enough” of black nylon), the designer had some wild cards to play. These took the form of fabulously contrasting block prints reminiscent of both Ed Roth, the Southern California hot-rod Picasso known as “Big Daddy,” and John Baldessari, the artist whose intellectual deadpan seems most closely aligned with Ms. Prada’s own.

Fendi, like Prada, is a family business. It was founded in 1925 on Via dei Plebiscito in Rome as a shop selling “baggage, trunks and umbrellas,” the designer Silvia Venturini Fendi explained before her show. Also like Prada, Fendi has a long history of women holding the reins of design and business. Ms. Fendi, like Ms. Prada, engages our times from an ironic position, if not always with quite Ms. Prada’s naturally subversive cast of mind.

Fendi men’s, fall 2018.CreditValerio Mezzanotti for The New York Times

Fendi is, after all, a fur house. Particularly at a time when science is able to produce artificial leather and designers like Andrea Incontri, working at Tod’s, are pursuing technologies that replace the use of animal pelts to produce handsome “shearlings”’ requiring no loss of animal life, it can seem a bit barbaric to offer chevron-cut travel coats or crocodile carry-on bags or bassinets made of sheared fur.

Yet, if one can suspend moral judgment (and if you like steak tartare) it is easier to judge on its design merits the formal dimensions of Ms. Fendi’s finely tuned show of oversize coats in Prince of Wales plaid, silk satin shirts, vaguely pervy raincoats, Eisenhower jackets, moonboots and umbrella caps.

And there is no certainly no disputing that, when it comes to stagecraft, hardly anyone in this town besides Ms. Prada is in Ms. Fendi’s league.

For Monday’s show, she designed a set resembling an airport terminal, replete with conveyor belt and arrival and departure signs. It made for an unintentionally, and somewhat macabrely, humorous commentary — during a season when a luggage disaster at John F. Kennedy International Airport condemned many editors and retailers on the fashion caravan to spend endless purgatorial hours tracking down missing bags — to watch models parade alongside a conveyor belt and then grab at totes and jewel boxes and trunks made from animal hides.

“I don’t know about you,” said a seasoned fashion wag seated alongside this reporter in the Fendi front row. “But I almost never check my mink weekend bag.”