The novel follows Ines, a young woman who enrolls at Catherine House, a fictional, intensely private school set miles off the highway behind a long iron gate. More exclusive than any Ivy League university, Catherine is tuition-free but demands total isolation from the outside world for three years. Students surrender personal belongings and outside contact. In return, Catherine promises extraordinary prestige, having produced diplomats, Supreme Court justices, and two presidents.
Ines wakes up naked in a bathtub on her first night, hungover and disoriented. She meets her roommate, Barbara Pearce, a small, bespectacled girl everyone calls Baby, who has smuggled a pet snail past the gate. They name the snail Billie Jean and declare themselves best friends. During orientation, Ines observes Viktória Varga, Catherine's enigmatic director, watching from a balcony. A filmed presentation explains the rules: students earn "points" for limited phone and mail privileges, the school provides all clothing and meals, and those who stray academically may be sent to the Restoration Center, which students call "the tower." At Catherine, all faculty carry the honorific "M." in place of traditional titles.
Ines has no ambition. Her backstory emerges in fragments: a beloved chemistry teacher, Mr. González, recommended she apply. During her senior year, Ines spiraled into reckless behavior that culminated in a hotel room where a girl died of an apparent overdose beside her. Ines fled without calling for help and ran for weeks before Catherine's admissions office tracked her down. She came not out of aspiration but because she had nowhere else to go.
In her first months, Ines skips classes and wanders the labyrinthine halls. She befriends Yaya Osmond, a bold girl who hates Catherine but refuses to fail out because her mother raised her to do "big, strange, ugly things." Classmates debate plasm, a purported new material thought to be the fundamental substance underlying all things, once celebrated as a revolutionary discovery whose credibility was damaged by scandal. Her advisor, M. Owens, tells Ines she is "empty" and trying to disappear but could succeed if she tried. Baby studies ferociously for the new materials concentration, Catherine's most exclusive discipline, and keeps a lock-picking kit at her desk to manage anxiety between study sessions. When Baby panics about a room inspection, Billie Jean's shell is found crushed.
Midway through the first year, the first-years undergo the "coming in," a nighttime ceremony in an underground ballroom. Viktória leads hours of guided chanting while concentrators fit plasm pins—slender metal instruments used to interact with plasm in the body—to each student's skull and stomach. One of Ines's pins comes loose, and she silently begs the concentrator not to fix it. She briefly experiences a terrifying flashback to the hotel room before surfacing. At the ceremony's end, Viktória's slight smile reveals she knows about the unfixed pin.
After Ines nearly fails out, Viktória summons her, reveals knowledge of her past, and sends her to the tower, a windowless room with only a bed, bookshelf, and playing cards. A concentrator brings plasm pins with meals, but Ines refuses them for days. He explains they function like guided meditation, realigning the plasm already present in the body. When Ines relents, she experiences a powerful interconnection with the house, then vomits violently, feeling as though she is purging all the poison of her past. Viktória visits, tells Ines her past life is over, and calls her "my beautiful girl." After five days, Ines goes to the library to work, marking a turning point.
Baby's mental state deteriorates. She confesses she cheated on a chemistry midterm and is sent to the tower, where she dies during the hottest day of summer. The grade dean announces that when someone "chooses to go," nothing can stop them. At Baby's memorial, Viktória says Baby is everywhere, "in our windows and trees and walls." Ines passes her finals, is accepted into the history of art concentration, and silently pledges to stay at Catherine with Baby.
In her second year, Ines settles into Catherine's rhythms, attending weekly communal chanting sessions and forming deeper friendships with Yaya, classmates Anna Montgomery and Nick Townsend, Diego Jimenez, a fellow art history concentrator, and Theo, a warm new materials concentrator. A class on Futurism introduces Umberto Boccioni's concept of "interior plastic infinity," joining an object's inner and outer realities, which resonates with Ines's growing understanding of plasm. In the library, she discovers a letter from Viktória about a student who died six years earlier, accompanied by a photograph of a boy with dark curls and a mole by his lip.
Theo shows Ines his secret project: a mouse whose wound has been kept in suspended animation by plasm pins connecting it to other objects. He explains plasm is not a substance but a network connecting all things. After a second pinning ceremony for second-years, Ines experiences profound dissolution, feeling herself part of the house, the floorboards, the sky. She walks to Viktória and calls her "Mother." As the feast ends, Ines spots Theo whispering with M. Neptune, the director of the new materials concentration, confirming Theo has joined his research team.
In her third year, Ines and Theo begin a romantic relationship. While he sleeps, she finds a blank white keycard in his dresser, the key to M. Neptune's private lab. She recognizes Sandy, one of M. Neptune's students, as Alexander, the boy from the old photograph. He is not dead but kept in suspended animation, moving through the house while concentrators monitor him.
After a session, Ines takes the keycard, puts on Theo's hoodie, and breaks into M. Neptune's lab. In a dim inner room, she finds cases of increasing size, each containing animals and objects networked via plasm pins. At the end of the room, the binder beside a large case reads "BARBARA PEARCE." Ines places her hand on Baby's case but cannot open it. She whispers "Hi, Baby" and weeps. Before leaving, she releases a rabbit onto the yard and returns the keycard.
Theo is sent to the tower days later: Security footage captured someone resembling him entering the lab, and his tagged keycard was logged. Ines confesses to M. Neptune and is taken to the tower herself. An aide confirms Theo was released an hour earlier and adds that Theo always insisted Ines was the one who broke in.
Viktória visits and explains that Baby and Alexander both chose to become experimental subjects. Catherine's mission, she says, is to discover how to make people "at home, forever." She frames their fates as liberation from the pain of living. When Ines asks if Theo knew what Viktória planned for her, Viktória confirms he suggested it. Outside the door, aides prepare a case just Ines's size. Viktória asks if she wants to undergo the process. Ines says no. Viktória tells her she will not be returning to her room.
Time passes. Yaya visits on graduation day, crying when she sees Ines. During a card game, Yaya slips a tension wrench and lockpick from Baby's old kit into the deck, taped to a Monopoly card. She tells Ines it is time to leave. After counting the days according to Yaya's instructions, Ines kneels at the tower's back door with the tools. The knob simply turns; the door may never have been locked. She walks to the loading dock, where Bunny, the dock manager, and Glo, the truck driver, are waiting. Bunny hands her a ham sandwich and civilian clothes. As the truck travels through the night, Ines lies on a stack of mattresses, knowing Catherine will haunt her forever, that someday a scent or sensation will transport her back, and she will be home again, and then gone. The truck stops at dawn. Footsteps crunch against gravel. Ines turns toward the opening door, raises her arm against the light, and the novel ends.