When you think of “The Odyssey,” your first free-association might not be four young women from the Middle East, the Balkans and Africa in a contemporary refugee camp in Greece.

But in a world-premiere adaptation presented by the Acting Company in association with Marin Theatre Company, Homer’s epic about a warrior trying to return home seems to secretly be about these women’s own journeys. Every wave and splash they felt, Odysseus did, too — a lovely point, but one the play underlines too forcefully.

四、Anoud(蕾拉Khoshnoudi),搅拌a thick, well-thumbed copy of Homer’s epic out of her backpack. She’s just bossy and visionary enough to enlist the group to act it out with her; after all, they have nothing better to do while they wait in limbo for their numbers to be called from a grainy loudspeaker. But soon she awakens in them a yearning to be seen in the story and as storytellers, an awareness that they’ve known this story all along.

In Lisa Peterson’s play “Odyssey,” which opened Tuesday, Sept. 5, retelling a founding narrative of Western literature is just one layer of plot. Another is watching Zee (Zamo Mlengana), Hana (Anya Whelan-Smith) and Béa (Sophie Zmorrod) get reborn from victims to artists.

Whelan-Smith’s Hana scours the lower depths of her voice, then hunches her spine, and boom, she’s an old shepherd. Mlengana’s Zee perches on a high throne, and her beatific, dignified smile could come only from Zeus. Zmorrod’s Béa pops her hips to morph into a sexy goddess, and it’s as if Charlotte from “Sex and the City” discovered her inner Samantha. Such moments of becoming electrify, the women recharting their life destinies from their cores outward.

Peterson’s choice of setting, racking up illuminating parallels between the women and Odysseus, trounces the notion that Homer’s poem is irrelevant or that its interpretative possibilities are exhausted. Here, both ancients and moderns travel to Greece on makeshift vessels amid stormy seas, not knowing when or if they’ll ever get home, whether home will be recognizable or family are still alive.

But this “Odyssey” makes those connections too didactically. Each time the women pause their rousing reenactment — where lights, by Russell H. Champa, make the path to Hades as eerily lit as the inside of a skull — to talk about their own lives, the play practically shakes you by the shoulders to insist, “See, it’s just like in ‘The Odyssey’!” Yet the women’s tales, tasking their audience with caring about something never mentioned before or again, almost never rise above tangents. It’s as if the play had interrupted its own broadcast to randomly sample some affliction from anywhere in the world.

“Odyssey” also suffers from an issue that’s dogged many recent Marin Theatre Company productions, which is a tendency to spout anodyne life lessons in the manner of a school assembly. When the women learn to offer each other the chance to play Odysseus, it’s partly to make the case that the hero’s journey belongs to everyone, but you can also practically see a subtitle announce, “Sharing is caring.”

The company has been without an artistic director sinceJasson Minadakisdeparted in March. Here’s hoping his successor is unafraid to program plays that explore the full, adult range of experience, in all its darkness, ambiguity and discord.

Reach Lily Janiak:ljaniak@sfchronicle.com