A philistine in the art film business, Jeremy Prokosch is a producer unhappy with the work of his director. Prokosch has hired Fritz Lang to direct an adaptation of "The Odyssey," but when it seems that the legendary filmmaker is making a picture destined to bomb at the box office, he brings in a screenwriter to energize the script. The professional intersects with the personal when a rift develops between the writer and his wife.

An industrialist and a pianist meet on a trip and fall in love. Through a quirk of fate, they are reported dead in a crash though they weren't on the plane. This gives them the opportunity to live together free from their previous lives. Unfortunately, this artificial arrangement leads to greater and greater stress. Eventually the situation collapses when they come to pursue their original, individual interests without choosing a common path.

Beautiful gold-digger Sonia mistakes Antonio, a waiter in a Neapolitan hotel, for Arab Prince Bey of Agapur and makes an appointment with him for the following day in Capri, and Antonio goes there behind the backs of his wife and mother-in-law. A lucky series of circumstances actually does transform him into the prince of the island.

The lonely wife of a workaholic husband on the magical Isle of Capri meets a charming and attractive young man. An exciting affair must end when word gets back to the husband and he becomes ill. In hopes of avoiding a scene, she passes her beau along to her stepdaughter, Monica.