When the history of the decline of American moviegoing is written, one savior will deserve mention: Wes Anderson.

During a period of churning audiences and a lemminglike rush toward streaming, the eight-time Oscar nominee has made movies that have reliably coaxed spectators back into brick-and-mortar theaters. Like Christopher Nolan and James Cameron, Anderson has become a reliable brand.

That brand — visually squared-off and symmetrical, tonally eccentric, referentially promiscuous, and unapologetically fetishistic — has often sacrificed meaning on the altar of an arresting image or arcane cultural allusion: Anderson and his creative ensembles clearly had a ball making recent retro-chic comedies like “The French Dispatch” and “Asteroid City.” Still, even while admiring the writer-director’s continuing commitment to elaborating on the signature he’s been perfecting since “Bottle Rocket,” it’s been increasingly difficult to detect any depth to the work beyond his own self-imposed proscenium arch.

Anderson’s films are often achingly beautiful, clearly rooted in nostalgia for a vanished but still dimly accessible material world, extravagantly, enchantingly theatrical. But even watching his delightful Oscar-winning 2023 short film “The Wonderful World of Henry Sugar” left one with a question that has only gained in urgency: When is Wes Anderson going to do what he was put on Earth to do and adapt “The Royal Tenenbaums” into a Broadway musical already?

A girl can dream (preferably in a showstopper of an I-want ballad in the first act). In the meantime, we can add another feature-length Anderson bonbon to the box: “The Phoenician Scheme,” a lighthearted picaresque that, in its own Andersonian way, manages to engage subjects like greed, morality and spiritual longing, albeit at arm’s length.

Like everything in Anderson’s world, that arm is clad in a bespoke, superbly tailored sleeve. As “The Phoenician Scheme” opens, industrialist and arms dealer Zsa-Zsa Korda (Benicio Del Toro) is flying somewhere over the Balkan flatlands in his private plane when the trip is suddenly interrupted; soon, Korda is plunged into an existential crisis, contemplating his own mortality and seeking help from his only daughter, a novice nun named Sister Liesl (Mia Threapleton), in organizing his sprawling network of shady deals. Chief among them: a multilevel plan for the country of Phoenicia, where Korda is determined to squeeze value from every last resource he can exploit.

Like all of Anderson’s movies, “The Phoenician Scheme,” which was co-written by Roman Coppola, isn’t driven by its cockamamie plot as much as its world-building: In this case, that imaginative universe is a reverie of 1950s kitsch, lovingly shot by Bruno Delbonnel on silky 35mm film stock. Once the game is afoot, its rules barked out with scattershot alacrity by Del Toro, the details get lost within a miasma of zigs, zags and colorful digressions: This is a shaggy-dog story groomed to look like a supremely poised poodle, complete with a pink bow on its tenderly coiffed head.

It’s a mad, mad, mad, mad world that Korda alternately navigates and dominates in “The Phoenician Scheme,” which features some familiar rep-company players from Anderson films past: Tom Hanks, Jeffrey Wright and Willem Dafoe are all on hand here, as well as Bryan Cranston, Michael Cera (affecting an impressively convincing Norwegian accent) and newcomer Threapleton, whose no-nonsense Sister Liesl gazes from under her snow-white wimple with a combination of innocence and knowingness. “Is this an act?” she keeps asking, although viewers suspect she’s been in on the answer all along. Many of Anderson’s most affecting movies have had attenuated families at their core (op. cit. Tenenbaums); “The Phoenician Scheme” joins that collection as a wry, wistful portrait of fractured love and the wreckage it leaves.

Threapleton has easily mastered the clipped, mannered dialogue-delivery system of a typical Wes Anderson chamber piece; luckily, she taps into emotion that is often absent from his most stylized outings. “The Phoenician Scheme” is such a whirligig tour through mid-20th-century history and politics that everything, including anti-colonialist movements represented by a revolutionary leader played by Richard Ayoade, is reduced to little more than a chic style point (those fezzes!). But even amid the eye candy, Threapleton and Del Toro manage to find some nutrition, in this case a soul being reluctantly tugged between God and mammon, filial duty and freedom, conscience and the rapacious amorality of capitalism unchecked.

“I don’t need my human rights,” declares the proudly stateless Korda, safe in the knowledge that his privilege will trump all. But what about reckoning with his human wrongs? “The Phoenician Scheme” possesses the absurdist humor, perfect posture and faultless elocution of all Wes Anderson movies. But it also possesses, of all things, relevance.

At its fleeting best — in its meditation on the transactional and the transcendent — this one feels like it’s reaching for something more than surface charm.

Three stars. Rated PG-13. At theaters. Contains violent content, bloody images, some sexual material, nude images and smoking throughout. 100 minutes.

Rating guide: Four stars masterpiece, three stars very good, two stars okay, one star poor, no stars waste of time.