In the experimental montage that opens “Persona,” a bare-chested teenage boy caresses a screen upon which the faces of two women slowly morph back and forth. It’s easy to imagine Todd Haynes being tempted to start his deep-as-you-want-to-go rabbit-hole drama “May December” the same way, seeing as how this endlessly fascinating movie focuses on the blurring of the lines between a Hollywood star (Natalie Portman) and her true-crime character (Julianne Moore), who was caught in a sexual relationship with a 7th grader at the age of 36. The movie wants to know: Can playing this Mary Kay Letourneau-like tabloid sensation really answer what makes such a woman tick?

A heady director whose entire oeuvre feels ripe for film-studies dissertations, Haynes makes movies not merely to be watched, but to be analyzed and deconstructed after the fact. From the rich Douglas Sirkian pastiche of “Far From Heaven” to the queer twist on classical “woman’s pictures” provided by “Carol,” his style can be chilly and distancing. Not so “May December.” As layered and infinitely open-to-interpretation as any of his films, it’s also the most generous and direct, beginning not with Ingmar Bergman references (those come later), but with footage of monarch butterflies. They’re symbols of transformation, too, but also something nice to look at (and listen to, underscored by a lush reworking of the piano theme from “The Go-Between”) before these two women meet.

As Gracie Atherton-Yoo, Moore plays a woman with a Teflon conscience who, even after more than two decades, is still deflecting public criticism. It didn’t help that there was a crappy TV movie made about the scandal at the time, which Haynes amusingly samples at one point. Now a grandmother (by her first marriage), Gracie hopes that a new indie film will bring some nuance to her story — which doesn’t seem especially likely, if Netflix’s “The Staircase” and other examples are to be considered. But she’s hardly the first to have optimistically accepted such an offer.

Gracie welcomes Portman’s Elizabeth Berry, star of a popular TV series called “Norah’s Ark,” into the Savannah home she shares with Joe Yoo (Charles Melton), the much-younger “May” to this woman’s “December.” Joe was just 13 when they fell in love. They were caught in flagrante delicto in the stockroom of the Georgia pet shop where Gracie and Joe both worked. A media circus followed, and their baby was “born behind bars,” as the gossip rags put it.

Haynes and screenwriter Samy Burch present that backstory in pieces, allowing audiences to form their first impressions of Gracie before discovering her crime. Tone is everything in movies like this, and Haynes goes out of his way to avoid the sensationalism that made “To Die For” or “Cry-Baby” so delectably campy. One of Gracie and Joe’s survival strategies — what Joan Didion called the stories “we tell ourselves … in order to live” — is to insist that they’re still in love, although private scenes find him texting flirtatiously with someone else. There’s clearly more to this relationship than meets the eye, and Elizabeth can only uncover so much of it in the handful of days she’s arranged to observe the Yoo family.

As Elizabeth goes about her research, trying to get into Gracie’s skin by interviewing her ex-husband and those who know her best, what follows isn’t merely a captivating deconstruction of an actor’s process. It’s a thorough dive into the psychology of everyone involved, not least of all the woman who’d be drawn to play such a role. “It’s the complexity, the moral gray areas, that are so interesting,” Elizabeth tells a high school acting class, somewhat alarmingly oblivious to her audience. Laying clues that will pay off later, she discusses the nuances of filming sex scenes to these immature teens, and doesn’t adapt her description of Gracie to the fact her daughter sits among the students. The same age gap separates Gracie from Elizabeth that existed between the woman and her victim. Will she truly be able to do this woman’s story justice?

“May December” operates on many levels at once, allowing audiences to speculate as to Gracie’s motivations (the reason we are drawn to movies like the one being made about her) even as we watch Elizabeth “become” her character. At night, she goes back to the local home she’s renting — “quaint,” by her description, posh by anyone else’s — and watches video auditions with the underage actors who could be her co-star, remarking that they’re “not sexy enough.” Her interactions with the real-life Joe become increasingly flirtatious, to the point one can’t help but wonder whether Elizabeth feels she needs to seduce him in order to understand Gracie.

On a meta level, Moore is also an actor playing a woman found guilty of corrupting a minor, which raises intriguing questions about reality and representation (à la “Kate Plays Christine”). Withholding moral judgment as best he can, Haynes keeps things more emotional than intellectual, trusting audiences to do that unpacking on their own. Though Portman has the more conceptual role here, Moore must set a benchmark for believability as the “real” Gracie: a woman who describes herself as “naive,” but is heavily invested in how she will eventually be portrayed — and slyly manipulative in getting her way (watch how she influences her daughter’s choice of graduation dress).

“May December” suggests a fictional version of last year’s where-are-they-now documentary “Subject,” about the way public attention can change the lives of those featured in movies, not always for the better. The more interesting transformation here occurs within Elizabeth, as the actor attempts to find her inner Gracie. At one point, Haynes positions Portman and Moore in front of a mirror as Gracie goes through the motions of applying her own makeup. Midway through the scene, they turn from staring directly out into the audience to seeing themselves reflected in one another’s eyes. Whatever intimacy these two women establish, Elizabeth isn’t interested in protecting Gracie so much as she is in arriving at the “truth” of her motivations. That’s the ineffable ideal of art, and one that is inevitably limited by the distance between an actor and her subject.