Jane Doe lives in the town of Remarkable with her remarkable father, a famous author; her remarkable mother, a famous architect; and her remarkable siblings — Anderson Brigby Bright and Penelope Hope Adelaide Catalina. Her remarkable grandmama is the mayor of the town.
In fact, everyone in Remarkable is gifted in some way, except for Jane and her Grandpa John. They are so ordinary that the other residents in town often overlook them. Jane's mother is building the new bell tower for the post office. The bells will ring a composition written by Remarkable's famous composer, Ysquibel, who has been missing for several years.
One night, Captain Achibald Rojo Herring, a pirate, comes to the house looking for Jane's mother. He wants to see the bell tower. Grandmama explains that the tower isn't finished yet, but she offers to let Captain Herring stay for dinner. Jane is impressed with the pirate's manners and his knowledge of music.
For years, Jane has been the only student at Remarkable's public school. The rest of the children attend the school for the remarkably gifted until the Gimlet twins — Melissa and Eddie — are expelled from the gifted school because they explode a paint bomb that turns the students and teachers blue.
In Jane's class, the twins habitually misbehave and drive the teacher, Mrs. Schnabel, crazy. Jane is happy because the teacher must now stay in the room instead of leaving to spend time in the teachers lounge. She's also glad to have someone to talk to at recess. The twins enjoy wreaking havoc and tell Jane about their plans to build a weather machine for the upcoming science fair. They also want to meet Captain Herring, thinking he must be a villainous pirate. They are disappointed to learn that Herring is actually very nice. Unbeknownst to them, however, three new pirates — Jeb, Ebb and Flotsam — have arrived in Remarkable and are looking for their old captain.
Jane's brother, Anderson Brigby Bright, has a crush on Lucinda Wilhelmina Hinojosa, so he paints a photorealistic portrait of her and makes Jane deliver it. He wants to invite Lucinda to the Science Fair Dance but is too nervous. He makes Jane ask her. As Lucinda's talent is music (she sings with perfect pitch), she is unimpressed with Anderson Brigby Bright's portrait. Since there will be music at the dance and it won't interfere with her search for the composer Ysquibel, she agrees to go with him. Jane convinces her brother that he should show his affection for Lucinda in a way other than painting. He decides to try singing instead. The rest of the town wishes he would stop practicing his song as his singing is horrible. No amount of criticism will convince him that he isn't as gifted with music as he is in painting.
The Grimlet twins come to school upset on Monday morning. They'd hoped Captain Herring would teach them how to be pirates, but he told them it was far too difficult. Mrs. Schnabel disagrees, saying she could do the job if they'd be willing to listen to her. The Grimlet twins take the challenge, and soon Jane's classroom is changed into the model of a pirate ship. The children learn how to "speak" pirate and must walk the plank (a board that sticks out of the ground floor window) if they misbehave. They must also write a report about a famous pirate.
Jane wants to do a report about Captain Herring but is told by the librarian that there is no such pirate. The librarian tells her that the only pirate by that name was a character in an opera by Ysquibel. The librarian offers a myriad of books about Mad Captain Penzing the Horrific, a woman pirate of world renown. Jane wonders whether Ysquibel and Captain Herring were once friends, which is why the composer named a character after him.
Later, Jane tells Grandpa John that she is frustrated with pirate lessons, especially knot tying, because they don't have the right ropes. Her grandpa promises to bring her some ropes if Jane will promise not to tell anyone where she got them. Jane brings the ropes to school, but the twins are not in classroom. They've skipped because they didn't finish their homework. They'd been too busy working on their weather machine for the science fair. The teacher tells Jane that she is not cut out to be a pirate, but that being an ordinary girl who loves dogs is a perfectly respectable thing to be.
The following day is a historic one for the town of Remarkable. Jane's mother will unveil her clock tower, and the gifted school will host the science fair and dance. The whole town comes out to celebrate the new tower. Everyone is excited, except for Lucinda, who has searched in vain for Ysquibel. She is heartbroken that the composer won't hear the bells play his song.
When the clock hands move to noon, however, the bells don't chime. The audience is stunned. Someone accuses Captain Herring of stealing the ropes for the bells because he's a pirate. Detective Burton Sly disagrees. Jeb, Ebb and Flotsam had hired him to find the captain, but instead he'd uncovered the fact that Grandpa John stole the bells' ropes. As he is arrested, Grandpa John orders Jane to find the ropes and cut them into tiny pieces so they can never be used.
Jane doesn't understand why, but she hurries to the school to do as he asked. She discovers her classroom torn apart, and Dr. Presnelda, the principal of the gifted school, turning it from a pirate ship back to a classroom. Dr. Presnelda explains that Ms. Schnabel is sitting at home, thinking about her actions. She then tells Jane that Ms. Schnabel is her sister, who was once Mad Captain Penzing the Horrific.
Jane asks Captain Herring to help her break her Grandpa out of prison. He explains that he's not really a pirate. He'd never wanted to be a pirate but had disguised himself as one when he wanted to take a break from writing music. He also tells Jane that the reason her grandfather stole the ropes is so the bells wouldn't play and lure Lucky, Remarkable's shy and elusive lake monster, out into the open. Grandpa John was afraid that all the publicity would scare the lake monster. He wanted to protect the monster. Before he can tell Jane more, Ebb, Jeb and Flotsam kidnap him and take him back to their boat. They stick Jane in a parrot cage.
Anderson Brigby Bright takes Lucinda Wilhelmina to the science fair dance, but she is still inconsolable about Ysquibel's absence from the bell tower celebration. Before he can impress her with his singing, a dreadful storm erupts, and they must run for cover. The bottom of the parrot cage falls out, and Jane searches for something in Captain Herring's house that will help her free her grandfather. Instead, she finds a carton of sour milk with a picture of Ysquibel on it. She realizes that Ysquibel and Captain Herring are the same person. Jeb, Ebb and Flotsam keep Captain Herring bound and gagged as they set sail in the storm, but Lucky, the lake monster, attacks their boat to rescue the captain who had often serenaded her with his violin. Ms. Schnabel dons her pirate clothes one last time to seek out the Gimlet twins, as she knows their machine is responsible for the storm.
In the morning, after the storm, Jane discovers that her grandpa has been released. The prison was needed to house Jeb, Ebb and Flotsam. Jane tells him about discovering Captain Herring's true identity. She imagines she'll be famous when she tells everyone in town about it. Grandpa John convinces her to keep Ysquibel's secret, however, as the man won't be happy if he's forced to always write music instead of doing other things. Grandpa explains that the people of Remarkable are so busy being talented, they often forget to be happy.
Detective Burton Sly finds Ms. Schnabel with the Gimlet twins' weather machine. He convinces her to go back to pirating, using the weather machine to help steer her boat. He also tells her where to find a crew — Jeb, Ebb and Flotsam. As a detective, he longs to try and capture Mad Captain Penzing the Horrific out on the open sea. Sometime later, Jane receives a package from her former teacher; inside is a puppy. A letter explains that the puppy had been aboard her pirate ship. As pirating is no life for a dog and since she knew Jane always wanted one, Captain Penzing sent the puppy to her. Although the dog is as unremarkable as she is, it is soon a beloved member of Jane's family.