If the Covid shutdown challenged marriages and other partnerships, it also proved, for many, a spectacularly bad time to be single. Because while overexposure to others and limited time for introspection can be a drag, the opposite can be far more dangerous.

That’s the takeaway, at least, from “Three Houses,” the latest offering from Dave Malloy, the composer/lyricist/playwright/orchestrator who became a critical darling and then, more briefly, a Broadway sensation with “Natasha, Pierre & the Great Comet of 1812,” an arty pop opera inspired by “War and Peace.” He won more acclaim with “Octet,” a chamber choir musical focusing on internet addiction; other credits include a four-part adaptation of “Moby-Dick” and “Preludes,” described in a press release as “a musical fantasia set in the hypnotized mind of Sergei Rachmaninoff.”

“Houses,” now making its world premiere under the helm of one of Mr. Malloy’s frequent collaborators, director/choreographer Annie Tippe, takes us inside the minds of three individuals who share the misfortune of entering the pandemic fresh from shattered relationships. Each seeks refuge away from home: Susan, a novelist in her 30s, flees to her grandmother’s house in Latvia, while the younger Sadie and middle-aged Beckett respectively hide out in New Mexico and Ireland.

Set in a mysterious, noirish bar, designed by the prolific collective dots, the musical also features a Wolf, who first appears as the human bartender/emcee presiding over an open mic night at which Susan, Sadie, and Beckett take turns spilling their tales of woe — mostly in song, as is Mr. Malloy’s wont. “So this is the story of how I went a little bit crazy,” each sings at the beginning.

Susan, who is played by the attractive, supple-voiced Margo Seibert, takes the microphone first, and is the most irritating. If all three central characters have bourgeois problems, it’s especially tough to watch this glamorous navel-gazer — costumed by Haydee Zelideth in a sparkly emerald dress — alphabetize her late grandma’s literary collection out of boredom without thinking of the nurses and delivery workers who toiled for long hours, often at great risk, in those dark days of 2020. 

In fairness, Mr. Malloy’s typically meandering score does Susan, and Ms. Seibert, no favors. Like numerous composers who clearly grew up enamored of Stravinsky, Copland, Weill, and Sondheim, but lacked the capacity for exquisite melody that made those names immortal, Mr. Malloy tends to write dissonant, fussy passages that strike me as recitative inching toward an aria but seldom getting there.  

Sadie, portrayed by an impish Mia Pak, gets a more engaging number toward the end of her stay at a traveling aunt’s house, where she occupies her time building a digital replica of her grandparents’ home. This was my favorite section, in part because of the presence of Zippy, a video game badger puppet — voiced and operated by J.D. Mollison, the actor cast as Beckett — who becomes Sadie’s wry confidante. (Ms. Pak manages the Latvian dragon puppet who emerges as Susan’s companion, and Ms. Seibert takes on Shelub, the spider puppet who crawls into Beckett’s life.)

There’s a sense throughout all this that Mr. Malloy is building up to a larger statement about connection, reinforced by the presence of a series of grandparent figures gracefully played by Henry Stram and Ching Valdes-Aran. By the time Beckett’s story wraps, and the Wolf finally reveals himself — with Scott Stangland, ominous and vaguely intimidating as the emcee, upping his game accordingly — this has been made plain, and Ms. Tippe guides her players through a dénouement that is undeniably touching.  

If the majority of “Three Houses” proves more uneven, devotees of Mr. Malloy’s work should find ample enjoyment here. Fans of cute puppet tricks will get a few kicks as well.