The story follows an Irish immigrant named John Lawless (Tommy Steele) as he applies for a butler position with eccentric Philadelphia millionaire Anthony J. Drexel Biddle (Fred MacMurray). Even though the family is a bit strange, Lawless soon learns that he fits right in. Mr. Biddle takes a liking to him immediately and \"hires\" him. For the rest of the film, Lawless serves as the narrator/commentator.
Mr. Biddle busies himself with his Biddle Boxing and Bible School (located in his garage) and his alligators in the conservatory. His wife, Cordelia (Greer Garson), stands by, accepting his eccentricities with a sense of pride and class. The two sons, Tony and Livingston (Paul Petersen and Eddie Hodges, respectively) are headed off to college, never to be seen in the film again. The daughter, Cordy (Lesley Ann Warren, in her film debut), is a tomboy of sorts that had knocked out all of her potential suitors with a single punch. She tires of her father\'s eccentric house and wishes to see what\'s beyond the Biddle manor.
Biddle lets Cordy go to a boarding school (after some prodding), where her roommate teaches her how to lure men with her feminine wiles, known as \"Bye-um-pum-pum\". At a social dance, Cordy meets Angier Duke (John Davidson, in his film debut) and falls in love with him. He tells Cordy that he is fascinated with the new automobile and wants to head to Detroit, Michigan to make his fortune separate from his family\'s fortune.
Cordy comes back to her parents\' home and tells them that she is getting married to Angie. At first, this is a difficult thing for Mr. Biddle to take. He does not want to give up his little girl. After meeting Angie, and sampling his Jiu Jitsu fighting skills, Biddle takes a liking to him and accepts the proposal. The family then makes arrangements for a very grand wedding.
The stress of the wedding plans and disapproving remarks from Angie\'s mother (Geraldine Page) cause Cordy to get lost in the fray. Not surprisingly, Angie feels the same way. But their ways of dealing with the stress differ, which leads them to fight and call off the wedding. This sends the entire family into upheaval. Biddle sends John Lawless after Angie.
John finds Angie at the local tavern, contemplating what he will do next. During a rousing song-and-dance sequence, John tries to convince Angie to go back to Cordy. At first, Angie is stubborn and thinks of other ways to get out of his fix, saying that he wants to join the Foreign Legion. A bar fight breaks out and Angie is hauled off to jail.
In prison, Biddle comes to bail Angie out. He then reasons with Angie and gets him to understand how much Cordy cares for him. Angie decides to marry Cordy after all. But, he becomes forceful, and elopes with Cordy to Detroit.