Veterinary assistant May Kennedy experienced a troubled childhood due to her lazy eye. Her only "true friend" is a glass-encased doll named Suzie, which her mother made and gifted May for her birthday with the adage "If you can't find a friend, make one." Her optometrist fixes May's lazy eye, first with glasses, then with contact lens.
May befriends local mechanic Adam and eventually begins dating him. She fixates on his hands, which she considers to be the most attractive part of him. May's lesbian colleague, Polly, also shows an interest in her. One day, May remarks that Polly has a beautiful neck. During their flirtation, Polly gives May a pet cat, Loopy.
May invites Adam to her apartment, where he shows her a film that he made for university, titled Jack and Jill. The film displays two young lovers who go on a picnic and end up eating each other. May becomes aroused by the cannibalism in the film. While passionately kissing, she bites Adam's lip, drawing blood. Disturbed, Adam abruptly leaves. May shouts at Suzie and shoves her in the cupboard.
May later begins volunteering at a school for blind children, where she takes a liking to a sullen young girl named Petey, who makes her a clay ashtray with the name "MAY" pressed into it. Abandoned by Adam, May gives in to Polly's advances and starts a short affair. May overhears Adam saying that he is glad he could get rid of her. Devastated, she visits Polly, but finds her with another girl named Ambrosia. When even Loopy refuses to come near her, an enraged May throws Petey's ashtray at her, killing her and shattering the ashtray. She develops delusions that Suzie is talking to her.
May takes Suzie to school, introducing her to the blind children as her best friend. The children struggle to take Suzie out of the glass case, ultimately shattering the case and injuring themselves and May. May returns home devastated with the ruined doll. The following day, she meets a young punk, who asks her if she wants to get some candy with him, which she accepts. May admires the tattoo on his arm. At her house, he discovers Loopy's corpse and calls May a freak. May breaks down and fatally stabs him in the head. After heavily contemplating her future actions, May claims she needs "more parts".
On Halloween night, May dresses in a homemade costume resembling Suzie, adopts a normal personality, and goes to Polly's house, where she slits Polly's throat with a pair of surgical scalpels. When Ambrosia arrives, May stabs her in the temples. Next, she visits Adam and his new girlfriend at his house. May murders both of them with the scalpels. At home, she designs her "new friend", a life-sized patchwork doll made from the punk's arms, Polly's neck, Ambrosia's legs, Adam's hands, his girlfriend's ears, and Loopy's fur for the hair. Using the broken remnants of the "MAY" ashtray to form an anagram, she names the doll "Amy". She realizes that Amy has no eyes and cannot "see" her, so she gouges out her lazy eye. Crying in pain and bleeding, she puts the eye on Amy's head and begs the doll to look at her. She collapses on the bed beside the doll, and caresses it. Her creation comes to life, and brushes her face affectionately with Adam's hands.
