When his millionaire father dies in an automobile accident, pompous American businessman Wendell Armbruster, Jr. must fly to Italy to claim the body. Arriving in Rome on a Saturday morning, Wendell immediately takes the train to Naples, followed by a boat trip to the resort island of Ischia, where his father died. On the way, plump Englishwoman Pamela Piggott approaches Wendell in a familiar way, something that he finds odd and annoying. Once on Ischia, Wendell is met at the dock by Carlo Carlucci, director of the Grand Hotel Excelsior, where Wendell’s father had spent a month-long vacation each summer for the past ten years. Insisting that he must have his father's body back in Baltimore by Tuesday for a VIP-studded funeral, Wendell is disoriented by Italian customs and bureaucratic red tape and puzzled by the obvious fondness that Carlo and other hotel staff had for his father. The accommodating Carlo is amused by Wendell’s American desire for quick results, and promises to take care of things, including acquiring a legally mandated lead-lined coffin. Just then Pamela comes to Wendell’s suite looking for Carlo and holding a batch of Italian governmental paperwork. When Carlo relates that Pamela’s mother, Katherine, was also killed in the car crash, Wendell expresses sympathy, thinking that Katherine and his father were merely casual acquaintances, but when Pamela lovingly takes her mother's silken nightgown and slippers from the bed, Wendell is shocked by the revelation that the pair had been lovers for ten years. Late that afternoon, Carlo drives Wendell to the town morgue, where he must identify Wendell, Sr.’s body and sign the first of many sets of legal documents. Pamela is also there, and Wendell is touched when she places a bouquet on Katherine’s body and another Wendell, Sr.’s. She suggests to Wendell that the couple would be happy to be buried side-by-side in a lovely cemetery on the hill, but Wendell is adamant that his father will be buried in Baltimore on Tuesday. While Pamela remains at the morgue, Wendell returns to the hotel and is visited by Bruno, a valet who tells Wendell that he loves America and lived there for several years before being deported. Bruno talks about the great romantic love that Wendell, Sr. and Katherine shared and describes their early morning nude swims. When Bruno mentions that he had taken many Polaroid photographs of them, Wendell deduces that he is being blackmailed. Just then Carlo comes to the suite to inform Wendell that the bodies have been stolen from the morgue. Assuming that Pamela is responsible, he storms over to her room, where, in his anger, he refers to her “fat ass.” She is incensed that he would accuse her of stealing the bodies and resents his insult, for which he apologizes, saying he actually prefers women with fuller shapes. As an apology, Wendell makes reservations for them to dine together in the hotel. That evening, the restaurant staff, who are delighted to see Wendell and Pamela, joyfully relate what their parents ate and drank and how much in love they were. Pamela also tells Wendell about their parents' affair, extolling the ten years of love the couple shared. During the evening, Armando Trotta summons Carlo, who relates to Wendell that Armando has the stolen bodies. Wendell and Carlo then drive with Armando to the Trotta family vineyard, the site of the car crash, where the family demands $3,000 to cover damages to their vineyard. Realizing that the family is taking advantage, Wendell tries to bargain but is bamboozled into paying the entire amount, which Armando’s father insists cannot be in U.S. dollars because of the sagging American economy. Exhausted from being awake for forty hours, Wendell wants to sleep when he returns to the hotel but is attracted to the strains of the orchestra, which is playing a romantic tune for Pamela. Because it is almost dawn, Pamela wants to finish the evening as their parents did, by taking a nude swim, and runs down to the hotel pier, dropping her clothes along the way. At first mortified, Wendell finally strips down and jumps into the sea, following her to a rock where they bathe in the early morning sun. Unknown to them, Bruno has been awakened by their antics and secretly snaps Polaroid photographs of them. When Wendell and Pamela finally say goodnight, she thanks him for the loveliest night of her life. Late that morning, when Wendell awakens, Carlo reports that they now have three coffins, the two they need plus one thought lost in transit. The only problem is that his nephew, who had sneaked into a closed government office to get some necessary papers, has been arrested. Promising that things will be settled soon, Carlo leaves, after which Bruno arrives with the compromising pictures of Wendell's father. Wendell tries to give him $100, but Bruno refuses the money, relating that what he really wants is a visa to America. Wendell says that he cannot help, but Bruno insists that one of his influential friends, like Henry Kissinger, could do it. He then tells Wendell that he has similar pictures of him and Pamela and that he has to flee because Anna, his Sicilian girl friend, is pregnant and insists that Bruno marry her. While they are talking, Pamela comes into the room to weigh herself and is delighted that she has lost three pounds despite gorging herself the day before. Meanwhile, Anna, who is a hotel maid and has been listening at the doorway, goes to Bruno’s room to steal his revolver. After Pamela leaves to go to town, Anna summons a valet to Pamela's room, and when Bruno opens the door, she shoots him to death. Because the murder is discovered while Pamela is sightseeing, Carlo has her things moved into Wendell's suite while the police investigate the crime scene. Carlo also gives Wendell Bruno’s nude photos to destroy, but as Wendell is cutting them up, he glances at them and realizes that he likes what he sees. Later, when Pamela returns to the hotel to learn that her suitcases are in Wendell’s suite, she assumes that he wants to have an affair and is both flattered and irritated by his presumptuousness. They argue over his American arrogance, but soon start to kiss. After spending Sunday evening making love, they awaken to breakfast in bed, which Pamela relishes. Wendell offers to buy things for Pamela but she refuses and reveals that, even though her mother was only a manicurist, she never let Wendell, Sr. know and never took gifts or money from him. Meanwhile, a U.S. Navy helicopter transporting diplomat Joseph “J. J.” Blodgett arrives on the island. J. J., whom Wendell has always regarded as a bore, has been summoned by Wendell's wife to expedite the transport of Wendell, Sr.'s body. J. J. telephones Wendell from the hotel lobby, leading to frenetic attempts by Pamela and Wendell to clear her belongings from the suite. When J. J. arrives, Pamela pretends to be giving Wendell a manicure. J. J.'s suspicions are aroused, until Carlo says that Pamela is his niece and suggests that J. J. take one of the hotel's virility-enhancing mud baths. Sadly realizing that J. J.'s presence means that he will have to leave Ischia right away, Wendell comes up with a plan: secretly bury his father and Katherine in the cemetery on the hill and use the third coffin to transport Bruno, whose dream it was to return to America. After a brief ceremony at the cemetery, Wendell suggests that the gravestones list the names “Willie” and “Kate,” the couple’s pet names for each other, and the family name of Carlucci. A short time later, as Wendell is about to board the helicopter with Bruno’s body in his father’s coffin, Carlo cheerfully informs Wendell that his father's suite will be available next summer from July 15th through August 15th. When Pamela promises that next year she will be "so thin," Wendell smiles and says if she loses even one pound, they are through.