It’s only fitting that a bar, replete with liquor and raised like an altar, presides over Dave Malloy’s “Three Houses,” which opened on Monday at the Signature Theater. Malloy’s music is, after all, intoxicating. Alcohol is the accelerant for the show’s linked monodramas. And hung over is how it leaves its pandemic-sozzled characters at the end of a dark karaoke night of the soul.

You may feel that way too: lost in a morning-after fog like Malloy’s three protagonists, each having radically relocated during lockdown. Susan (Margo Seibert) found herself in her dead grandmother’s ranch home in Latvia, pointlessly alphabetizing the library. Sadie (Mia Pak) moved into her auntie’s New Mexico adobe, where a life-simulation game akin to Animal Crossing was her only companion. Having holed up in a “red brick basement in Brooklyn,” Beckett (J.D. Mollison) soon turned into an Amazon shopaholic.

As each now takes the open mic at the metaphysical bar to sing about going “a little bit crazy living alone in the pandemic,” it becomes clear, though, that more was at play. Encouraged by a bartender not incidentally called Wolf (Scott Stangland) — “don’t be afraid to go deep,” he says — they reveal to us, and perhaps to themselves, that Covid wasn’t the only threat to their well-being. Love, too, was a lockdown.

A recent seismic breakup is part of all their stories. Susan’s ex, Julian, moved to another state for work. Sadie’s Jasmine kept “messing up” household routines with her spontaneity. Beckett did not feel safe letting his wife, Jackie, see fully “the darkness within” him. That these accusations are so transparently thin does not weaken their effectiveness as defenses — or, because we recognize the behavior, as storytelling.

But Malloy’s attempt to cross-reference the stand-alone 30-minute stories with psychological and literal echoes palls. It’s easy enough to write off the twee alliteration of the three J-named exes as a kind of light rhyme or fairy-tale resonance. Same with the eight jugs of red currant wine in Susan’s tale that become eight cases of mezcal in Sadie’s and eight bottles of plum brandy in Beckett’s. Why eight? Why not? The point is that people drink heavily in isolation.

The meaning of the more ornate linkages is less clear. Each segment includes an obligatory puppet — a Latvian house dragon, a video game badger, a creepy spider, all designed by James Ortiz — that feels more like a stab at theatrical variety than an expression of a relevant human need. (Even so, Annie Tippe’s staging grows monotonous.) The bar’s orange-vested waiters (Ching Valdes-Aran and Henry Stram) reappear as various loving grandparents, indistinguishable despite their accents. But all the characters seem to have been reverse engineered from templates, suggesting structural desperation.

Such problems need not be inevitable in a triptych bound by theme (loneliness) and mood (melancholy) instead of plot or character. Malloy’s exquisite “Octet,” from 2019, directed by Tippe in the same space at the Pershing Square Signature Center, avoided the feeling of false connection, even with five more protagonists in the mix. But since “Octet” was specifically about false connection as experienced online, the form fit the function. Here it does not, despite strenuous if cryptic efforts.

For many, it will be enough compensation that Malloy’s music remains as hypnotic and embracing as ever, performed faultlessly by the cast (especially Seibert) and a busy quartet (violin, cello, French horn, keyboards) under Or Matias’s musical direction. A close-harmony coda, accompanied only by a hurdy-gurdy drone, specifically recalls the a cappella wonders of “Octet” and the hushed beauty of the title song of “Natasha, Pierre & the Great Comet of 1812.”

And if the lyrics are sometimes too thick with metaphors, they are also sometimes gorgeous and trenchant. I sighed at lovely phrases like “The air is latticed with birds,” perhaps especially because I’d been primed for poetry by Christopher Bowser’s dreamlike, rich-hued lighting. Glowing, flickering or suddenly illuminating a weird corner of the set (by the design collective dots), it seems to be wired directly to the music.

But intermittent gorgeousness is not, for me, a sufficient substitute for substance. What is “Three Houses” trying to say, or have us experience, about living through the pandemic — beyond the usefulness of eight quantities of liquor?

I could imagine Susan, Sadie and Beckett, in the disintegration of their social selves, as warnings to establish solid connections, or to repair frayed ones, before fate makes both impossible. But I could also imagine the opposite: that their disintegration — Beckett stops bathing and builds a clochán fortress from his Amazon boxes — is how they discover a need for connection in the first place: a connection that outweighs the discomforts of relationship.

Either way, it comes to the same bleak thing. As hinted by the title — and by naming the bartender Wolf — “Three Houses” is about being insufficiently prepared for the day when disaster comes to blow our house down. No structure, dramatic or otherwise, will save us on its own.

Three Houses
Through June 9 at the Signature Theater, Manhattan; signaturetheatre.org. Running time: 1 hour 40 minutes.