“Complete Unknown” opens with a montage of scenes from one woman’s bizarre, erratic existence.

She’s a free-spirited hippie one moment and an E.R. nurse the next. She’s a vamping magician’s assistant, but also a buttoned-up office worker. Who is this chameleon and why does she have so many identities?

That tantalizing question is enough to hook a viewer. Whether the movie maintains its hold is another matter.

In her latest life, the shape-shifter, played by Rachel Weisz, has morphed into scientist Alice Manning, and we see her deliberately trying to orchestrate a seemingly chance encounter with a tightly wound environmental lobbyist, Tom (Michael Shannon). Flirting with Tom’s co-worker to score an invite to her target’s birthday party is clearly not the shadiest thing she’s done. But she gets her wish and in quick succession we learn that Tom knew Alice — or Jenny, rather — when the two were involved in college.

That was before she disappeared one day without a word. Understandably, the semi-happily married Tom is confused and a little angry to find his former flame crashing his soiree.

“This is crazy. You’re alive,” he says once no one else is listening. “You thought I was dead?” she asks, sounding almost amused.

The movie then unfolds over the course of one night as Tom and Alice wander the streets of New York as they grapple with complementary problems. Tom’s wife, Ramina (Azita Ghanizada), wants to move to California for a graduate program, but he’s always been resistant to change. He even lives in the house where he grew up. Alice, meanwhile, might be ready for some stability, which is why she tracked down Tom — one of the few people who knows her from her first life.

And so what started as a thrilling thought experiment suddenly turns into something along the lines of “Before Sunrise.” Man and woman walk around all night, deep in conversation with occasional detours. At one point they wind up in the apartment of a woman (Kathy Bates) who injured herself while walking her dog, and both Alice and Tom pretend to be doctors. The tonal shift feels like a bait and switch, although the moody lighting and enigmatic music tries to rekindle the air of mystery long after all the secrets have been revealed.

Director Joshua Marston (“Maria Full of Grace”) wrote the script with Julian Sheppard, and the dialogue gets a significant boost from the movie’s magnetic leads. Weisz creates sympathy for her puzzle of a character, whose life seems both romantic and horribly deceitful. Shannon, meanwhile, aces the role of a curmudgeon — he appears to be in physical pain every time he cracks a smile.

Even if it’s not quite as thrilling as it first seems, “Complete Unknown” poses questions that practically beg for animated conversation about the fantasy of leaving it all behind — and what that might look like if someone actually did it, again and again. It’s a compelling issue, but this drama proves one thing: A movie can reinvent itself, too, but doing so mid-film isn’t easy to pull off.