After rehearsing his television show, singer Johnny Nyle is greeting his rapturous teenage fans when he is served with a subpoena. Johnny goes to the office of his former Navy colleague, attorney Adam Calhorn Shaw. The stiff, humorless Adam, who comes from a distinguished family, is meeting with his law partners, Grenville, Griswalde and Tremaine, who are advising him on his upcoming congressional campaign. Adam admits Johnny, who says that his former agent is suing him for back commissions, and agrees to help him, instructing him to come by his home later that afternoon. Adam then goes to the nursery to complain about some peach trees he bought for his garden. There he meets an attractive young woman named Athena Mulvain, who tells him she is a numerologist and offers to help him mulch the peach trees. Athena's offbeat ways make Adam uneasy, however, and he declines her offer. Later, Adam is at home having a cocktail with his fiancée, Beth Hallson, when the outspoken Athena shows up. After Beth leaves, Athena happily mulches the peach trees, then gives Adam a big kiss. On her way out, Athena passes Johnny and announces her intention to marry Adam. After a quick numerological analysis, Athena determines that Johnny would be a perfect match for Minerva, one of her six sisters. Leaving the paperwork for his case in Adam's mailbox, Johnny impulsively goes with Athena to meet her sister at the family's health food store. The following morning, Adam is surprised to find Athena back at work in his garden. Beth drops by and reacts jealously to Athena's presence, and Athena slips away before Adam can speak to her. After Adam's secretary tries in vain to track Athena down, Johnny comes by the office and mentions his own encounter with Athena, and tells Adam where to find her. That evening, Adam goes to the Mulvains' hilltop home, where he finds Athena's sisters dancing in the moonlight while scantily clad muscle men lift weights in the courtyard. Adam meets the robust Grandpa Ulysses, a health food and exercise enthusiast, who introduces him to Ed Perkins and Bill Nichols, the body builders he is training for the Mr. Universe competition. While the family and friends sit down to a supper of peanut burgers, Adam takes Athena aside and tells her there can be no relationship between them. Athena asks Adam to kiss her goodbye, and their embrace quickly grows passionate. When Adam returns home after midnight, bearing an bouquet of ginger blossoms he has been instructed to eat, Beth graciously ends their engagement. Grandma Salome stays up most of the night working out an astrological chart for Adam and Athena, and although she sadly reports that the stars disapprove of Adam's lifestyle, Athena refuses to give up on him. The following day, Adam's casual dress and chipper demeanor puzzle his partners, who demand to know more about Athena. Meanwhile, Athena brings her sisters to Adam's house, and they set about redecorating it for greater cosmic harmony. When Grenville and Tremaine see the house, they tell Adam he must get rid of Athena in the interest of his political career, but Adam assures them that Athena can behave like other people when necessary. To prove it, Adam brings her as his date to an elegant political reception that evening, and Athena charms the guests with her beauty and singing. However, the vegetarian Athena gets into a quarrel with Beth in the buffet line, and flees to the nightclub where Minerva is watching Johnny perform. After comforting her sister, Minerva tells Johnny that if Adam and Athena split up they must, too, as the stars dictate that Athena must marry first. Adam is waiting for Athena when she returns home, and declares his love for her. As he leaves, Grandma cautions Adam to avoid crowds the next day. However, Adam shows up at the Mr. Universe contest the following evening and watches as Grandpa presides over the competition, which Ed narrowly wins. At the press conference afterward, Ed jealously warns Adam to stay away from Athena, and Adam uses his Navy judo training to throw the strong man to the ground. With the television cameras rolling, Athena angrily breaks up with Adam. Later that evening, Adam is visited by his partners, who gravely proclaim his political career dead and offer him an assignment in Bolivia. Johnny then comes by and informs Adam that Athena has consented to Grandpa's wish that she marry Ed. The two men immediately head to the Mulvain home, and Adam criticizes Grandpa for being judgmental. The following morning, Athena comes to Adam's house and says her grandparents agree that love will help them overcome their differences. Later, Adam, Athena, his business partners and the entire Mulvain clan happily sit down to a banquet of fresh fruit.