Director Neil Jordan has done well by werewolves once before in his career with The Company of Wolves, and vampires twice in Interview With the Vampire and Byzantium. With Greta, his first feature in the six years since the latter’s release, he ventures into psycho-stalker-thriller territory, with less successful results.

Jordan and co-scripter Ray Wright (Case 39, the Crazies remake) start the scenario well, having come up with an effectively devious variation on the rom-com “meet cute.” Frances McCullen (Chloë Grace Moretz) is a young woman recently transplanted to New York City from Boston who’s doing pretty well, all things considered; her waitressing job is at a high-end restaurant, and she shares a beautiful, spacious loft with her BFF Erica (Maika Monroe), who got it as a birthday present from her wealthy folks. Frances still holds onto her small-city values, and when she finds a handbag abandoned on the subway, she rejects Erica’s idea to keep the money they find inside and decides to return it to its owner because “Where I’m from, that’s what you do.”

That leads her into the Brooklyn dwelling of Greta Hideg (Isabelle Huppert), a widow who is delighted to get it back, and to discover a new potential friend in Frances. Greta is missing her daughter, who’s away in Paris, and Frances is still grieving the recent death of her mother, so the two bond emotionally, and a little too quickly in Erica’s view. “You’ve totally adopted this woman,” she says, not long before Frances discovers evidence that her and Greta’s meeting wasn’t as random or coincidental as it first seemed. This revelation is accompanied by the dramatic/scary swelling of Javier Navarrete’s score, as is an early moment in which Greta obsessively peruses Frances’ Facebook. They’re early signs that Jordan is poised to take the movie over the top, but he never quite makes the leap.

Greta is both a genre piece and a cautionary tale about letting a stranger into one’s life too quickly, and on both levels it unfolds in familiar ways. Greta, whose neediness becomes pathological, begins stalking Frances at home and at work, seemingly poised on the knife-edge of violence. To the film’s credit, the initially naive Frances doesn’t recede into shrinking violet-dom but proactively does her best to get Greta out of her life, with Moretz bringing an appealing mix of ingenuousness and pluck to the role—though of course, neither the cops nor appeals to Greta herself do much good.

There’s a lot of “of course” to the movie’s narrative, in fact, as it wends a predictable path from bad to worse for our heroine. Greta has been put together well (Seamus McGarvey’s alternately luminous and ominous cinematography is particularly fine), which makes it a shame that the parts too often feel second-hand. In particular, the focus on a deranged co-dependent relationship between two women in New York can’t help but recall Single White Female, which was more psychologically complex and acute. (Not to mention more authentic in its settings; from the opening scenes on the subway, it will be clear to anyone familiar with the city that much of Greta was shot in Toronto and the Irish capital, Dublin for NYC.) Fans of Takashi Miike’s Audition will recognize certain key bits of iconography as well.

Since the story is told from Frances’ point of view, we’re not let deep enough into Greta’s head until the film’s second half, when her threatening fixation crosses over to dangerous action, and Huppert gets the chance to go full unhinged. The veteran actress is certainly game to take the trip to bugnuts crazy, and has enough moments of delirious delight to make one wish the film would make the same commitment. Instead, Jordan teases us with the possibility that his movie will fly off the rails and go as batty as its villain, yet he just as often pulls back, as if determined to keep Greta in “respectable” territory.

In that goal, he is let down by his own script, which stretches credibility until it snaps. Once Erica and others in Frances’ life realize just how much danger Frances is in, instead of making a concerted effort to help her, they set off on solo courses for the sole reason that if more than one of them were present at a couple of key moments, the film would come to a premature end. Late in Greta, Jordan regular Stephen Rea turns up as a detective, and those familiar with the psychothriller form will be able to discern his character’s entire trajectory from his first scene. Under the circumstances, it’s not giving too much away to note that not once but twice, someone succeeds in putting Greta down, but makes the common movie mistake of not doing a good enough job, allowing her to lurch back to crazed life a couple of minutes later. Greta the movie is similar, veering between subdued and moments of insanity, to disappointing ends.