The story is framed as a historical account written by Dr. G. Edwina Candlestank, a self-described mad scientist who addresses the reader directly with humorous footnotes and asides.
In the fictional town of Antiquarium in 1911, the Porch sisters, Gertrude, Eugenia, and Dee-Dee, are misfit students at Mrs. Wintermacher's School of Etiquette for Girls. The three are not biologically related but were adopted as infants by Desdemona and Ansel Parquette. The Porches care nothing for etiquette: Eugenia likes explosions and rocks, Dee-Dee likes building machines, and Gertrude, the oldest, is fascinated by animals and insects. When Gertrude demonstrates a posture-improving invention called the Bat Straightener, which uses a harnessed live bat, chaos erupts and all three are expelled, marking their ninth expulsion from an Antiquarium etiquette school.
Each sister discovers a gold-lettered invitation in her backpack for a place called "The Marjory Questions School of Etiquette for Young Ladies." The invitations smell faintly of tomato sauce, triggering a memory for Gertrude: At age seven, she found a scroll referencing the legendary Millicent Quibb inside a moon snail shell on the beach, carrying the same scent. When the Parquettes threaten to send the Porches to a harsh boarding school in Austria, Gertrude presents the invitation as proof of local acceptance. Aunt Desdemona, attracted by the free option, agrees.
The Porches walk to 231 Mysterium Way, a decrepit mansion where a sign made of living moths reveals the school's true name: The Millicent Quibb School of Etiquette for Young Ladies of Mad Science. Millicent Quibb herself appears, six feet tall with chaotic hair and a stained lab coat, a figure local children's rhymes have long warned about. Her blue hermit crab, Antonio, lassos the sisters and puts them to sleep. Millicent assigns each a mad science discipline: Gemistry (rocks and unusual substances) for Eugenia, Fryzzics (impossible machines) for Dee-Dee, and Unnaturalism (unnatural creatures) for Gertrude. She claims the town faces danger from evil forces and pleads for their help. Eugenia insists they leave, but Gertrude feels physically unable to walk away and agrees to one expedition.
Millicent reveals that Antiquarium was once the Capital of Mad Science of the Northern Hemisphere during the Heyday of Mad Science (1671–1761), before the Great Fire buried the old establishments and outlawed the practice. She identifies recent damage around town as signs that the Krenetics Research Association (KRA), an ancient cohort of evil mad scientists, has returned. At Cobblestone Alley, Gertrude spots a hole ringed with tooth-like markings. Millicent identifies it as a bite from the Kyrgalops, a giant stone-eating worm originally bred by the KRA and thought extinct. Mayor Majestina DeWeen, a glamorous politician Gertrude idolizes, addresses the press about the vandalism.
At the Mad Science Library, hidden beneath a swamp, the group finds a taxidermied Kyrgalops display with one egg missing and a purple feather inside the case that Gertrude recognizes from Mrs. Wintermacher's hat. Using a Spy Snail named Lou, which transmits everything the snail perceives to its wearer, the Porches spy on Wintermacher and discover she is keeping a live baby Kyrgalops. On the phone, Wintermacher confirms she will contain the worm until Sunday, saluting with a KRA tattoo and invoking the founder, Talon Sharktüth.
A note from Millicent explains they must retrieve the diary of Dr. Fifi Bubblegumme, the Kyrgalops's original creator. After a training period in which each sister hones her discipline's skills, the group infiltrates a spoon shop concealing the entrance to Bubblegumme's underground laboratory. Inside, they find thousands of diaries. When millions of silkworms pour from the ceiling, Gertrude repels them with high-pitched singing, a technique from training, and Dee-Dee constructs a conveyor belt to transport the diaries out.
Bubblegumme's diary reveals that the worm's favorite food is the bichon frise, it can be trapped in a cage of Prismuth (a rare mineral), and it becomes docile near the Panacea Slug, a part-human, part-slug creature whose slime cures disease. Millicent gives each sister a packet of Rapier Vine seeds, emergency provisions that sprout dangerous vines when consumed. Mrs. Wintermacher, eavesdropping outside, learns the worm is attracted to bichon frises and plans to use the dogs as bait.
Millicent, disguised as "Marjory Questions," visits the Parquettes and discovers that Aunt Desdemona's garish rainbow brooches are made of Prismuth. Eugenia and Dee-Dee use the stolen brooches to build a cage. Returning to Wintermacher's school to trap the worm, they find it gone. Through a tunnel, they observe a secret KRA meeting where the masked leader announces a dog beauty pageant at the fairgrounds the next day to draw bichon frises. The KRA's true goal is "Operation OTV," or Open Talon's Vault: The Kyrgalops will bite through the entrance to Talon Sharktüth's buried vault, where the founder fled centuries ago with an elixir of immortality.
Gertrude warns Mayor DeWeen, who seems sympathetic but calls the Parquettes instead. Lavinia-Steve, one of the Parquette daughters, has told the family about the stolen brooches. The Parquettes lock Gertrude in a turret and her sisters in their shed. At her lowest point, Gertrude exchanges messages in window dust with her sisters. Inspired by a bat drawing from Eugenia, she feeds a colony of bats in the turret rafters, dons the Bat Straightener harness, and the bats fly her to the ground. She frees her sisters, and Millicent arrives on her Flycycle, a flying motorcycle shaped like a housefly, with the Prismuth cage.
At the fairgrounds, Mrs. Wintermacher hurls the Prismuth cage into the chlorinated swimming pool, destroying it. Gertrude realizes Wintermacher learned about the cage from Mayor DeWeen, confirming the mayor's connection to the KRA. Gertrude swallows her Rapier Vine seeds, and the vines crack the padlock on the show ring, freeing trapped dogs and people. Millicent tries to lure the Kyrgalops away but fails, and Majestina publicly blames Millicent, turning the crowd into a mob. Eugenia and Dee-Dee create a diversion so Millicent can flee, but she disappears. Gertrude fashions the limp Prismuth into a lasso, sings in her deep baritone to attract the Kyrgalops, and the worm bows to her, pressing its forehead to hers. She mounts the creature and rides it into the ocean at Red Dune Beach, where her sisters rescue her on the Flycycle.
In the aftermath, the KRA's masked leader banishes Mrs. Wintermacher for incompetence, then privately vows devotion to Talon Sharktüth, though her identity remains hidden from the reader. The Parquettes sentence the Porches to deportation to the Versagenschule, or "School for Failures," in Austria. During the confrontation, Aunt Desdemona accidentally reveals the family is "being paid handsomely" to watch the children. Gertrude stands tall and says "You're welcome," asserting that the Porches saved them.
Before leaving, Gertrude redirects their car to Mysterium Way, but Millicent's house is gone, with only a hole in the grass and a single electric-blue rose petal remaining. After weeks of travel, the Porches arrive at the Versagenschule, a castle on a snowy Austrian peak, and are locked in a damp cell. Eugenia reveals she smuggled their mad science textbooks by wrapping them in Taffetteen, a special fabric used for disguises. The sisters vow to study, return to Antiquarium, and fight. Outside the castle, Millicent shivers beside her Flycycle by a frozen lake, vowing to rescue her pupils. In the epilogue, the male Kyrgalops, a hamster-sized parasite that had lived inside the female, emerges from the sea and begins gnawing at the metal door of Talon Sharktüth's vault, set to finish by morning.