To say Dave Malloy’s influences are eclectic is to severely understate the case.

The 43-year-old writer-composer’s best-known work to date, “Natasha, Pierre & the Great Comet of 1812,” is a gleefully anachronistic (but rarely ironic) “electro-pop opera” based on a small section of Tolstoy’s “War and Peace.” Another Malloy musical, “Preludes,” looks to another bit of Russian history; it’s set inside the mind of composer Sergei Rachmaninoff as he undergoes hypnotherapy to cure his writer’s block, and mixes his Romantic melodies with electronic beats.

‘Ghost Quartet’: 3.5 out of 4 CST_ CST_ CST_ CST_ CST_ CST_ CST_ CST_ When: Through Aug. 12 Where: Stage 773, 1225 W Belmont Tickets: $30 Info: stage773.com Run time: 1 hour 30 minutes, with no intermission

And Malloy’s “Octet,” which premiered Off Broadway in New York earlier this year, is an a cappella musical about a support group for internet addiction. In a program note and in interviews about the show, Malloy cited inspirations as varied as Walt Whitman, “A Chorus Line,” the experimental rock band TV on the Radio, and the classic video game “The Legend of Zelda.”

None of these Malloy works has been seen in Chicago yet; even “Great Comet,” which had a well-reviewed Broadway run and earned a dozen nominations at the 2017 Tony Awards, never launched a touring production. (A report in Variety last year suggested the Broadway producers were holding on to the show’s rights in hopes of launching sit-down productions in other U.S. cities, but they have yet to materialize.)

But Chicago finally gets a taste of Malloy’s unique sensibilities with Black Button Eyes Productions’ enchanting staging of “Ghost Quartet.” This 2014 work is classified as a “song cycle” or, to quote Malloy, “a live concept album.” Think of it as not so much a traditional musical but a mood.

Yet if there’s not a standard, linear narrative with a beginning, middle and end, narratives are nonetheless the driving concern of the piece’s meditation on death and how we deal with it. Malloy borrows bits of stories from across centuries: Scheherazade and Dunyazad of “Arabian Nights,” Rose Red as rendered by the Brothers Grimm, Edgar Allan Poe’s “The Fall of the House of Usher.”

These stories and their characters flow into and over one another in the course of “Ghost Quartet,” along with other elements of Malloy’s creation, in a manner that feels intentionally disorienting. Each new scene and song is announced as if it’s a track listing on a double LP (“Side 2, Track 4: ‘Fathers & Sons’”), which provides some sense of structure, but there’s no telling as that scene begins which story or which century we might be in, or which version of their multiple characters the actors might be playing.

Rachel Guth, a fresh-faced young actor who can convey innocence and edge simultaneously, turns out to be the sort-of protagonist, as her Rose seems to live many lifetimes across the centuries. She also appears to reincarnate as her own child on more than one occasion, but you learn not to worry too much about the details pretty early on. The first version of Rose we meet, a 21st-century woman who walks into a camera shop run by a woman who may have been her sister in a previous life, expresses her own confusion at what’s happening. “It’s OK, my dear,” replies Pearl (Amanda Raquel Martinez). “This is a circular story.”

That loose, metatextual vibe goes a long way toward selling the stories’ fluidity. Certain motifs recur — a soldier, a bear, a dead sister — both as beacons to keep us following Malloy’s long and winding road, but also as signposts about the malleability of the stories themselves. Psychologists, philosophers and scholars of comparative mythology and religion have argued that there are only a small number of archetypal plots and characters. But we’re constantly, and endlessly, reinventing and readapting them, tailoring them to our cultural moment or mindset.

Not that “Ghost Quartet” is breaking out Joseph Campbell and Carl Jung. This is a goofily macabre show, the kind that contains a song (“Side 1, Track 7, ‘Any Kind of Dead Person’”) that rates the various types of undead — vampires, zombies, mummies, White Walkers — and concludes “I just wanna be a ghost / and go wooooo all night long.”

It’s the kind of show in which the performers — who in director Ed Rutherford’s production include T.J. Anderson and Alex Ellsworth in addition to Guth and Martinez — call each other by their real names when they’re not in character. It’s the kind of show that suggests at one point that the ghost of the great jazz pianist Thelonious Monk, who died in 1982, might be living in 14th-century Persia, and you accept the possibility with a smile.

Those four charming performers, by the way, are all talented multi-instrumentalists as well, accompanying themselves on instruments that include piano, cello, acoustic guitar, trumpet, accordion, autoharp and percussion. That’s all in service of Malloy’s songs, which employ wryly self-aware lyrics and a blend of styles that leans toward Americana and folk: think part Tom Waits, part Mountain Goats, with healthy dashes of Wilco, the Decemberists and Gogol Bordello. The show would be just as at home at the Old Town School as it is at Stage 773. They may wanna be ghosts, but these apparitions are guaranteed to liven up your summer.

Kris Vire is a local freelance writer.