In the prologue, gangster Angelo "Snaps" Provolone promises his dying father, played by Kirk Douglas, that he will leave the world of crime behind and "go straight." A month passes, and Snaps awakens in his luxurious mansion, ready to embark on a significant day. He has an important meeting lined up with several prominent bankers, aiming to donate a considerable sum and gain a position on the board of trustees, ultimately striving for a legitimate career in honor of his father's wish.
Snaps's young and optimistic accountant, Anthony Rossano, arrives and reveals that he is smitten, requesting a staggering 250% raise. To Snaps's shock, the object of Anthony's affection turns out to be none other than Snaps’s daughter, Lisa. Furious at the prospect of his daughter marrying Anthony, Snaps quickly seeks out Lisa, who is spoiled and longs to explore the world but is thwarted by her overprotective father. In an attempt to gain independence, she concocts a scheme, misleading her parents into believing she is pregnant. Snaps assumes Anthony is the father, only to be further flabbergasted when Lisa reveals the actual father to be Oscar, the former chauffeur currently abroad.
The plot thickens as Anthony discovers that the woman he has fallen for, Theresa, is not actually Snaps's daughter as she claimed. Before this revelation can settle in, Snaps cunningly persuades Anthony to marry his true daughter, Lisa, who is supposedly expecting but lacks a husband. Both Lisa and Anthony are less than thrilled with this rushed arrangement, especially when Lisa discovers a heartfelt connection with another man, Dr. Thornton Poole, a dialectician working with Snaps.
Meanwhile, police lieutenant Toomey, suspicious of Snaps's activities, is keeping watch on the mansion, convinced he will find Snaps colluding with Chicago mobsters. On another front, rival mobster Vendetti is also plotting against Snaps, under the impression that a significant meeting is imminent. Vendetti plans an ambush just as Toomey intends to raid the place to catch Snaps red-handed.
In the midst of this chaos, Anthony searches for Theresa while Snaps has a serendipitous reunion with his mansion's new maid, Roxie. It turns out that Roxie is an old flame of Snaps, and as they reminisce about lost opportunities, the plot takes another twist: Theresa is revealed to be Roxie's daughter, making Snaps her biological father.
The anticipated meeting with the bankers is disrupted by the sudden arrival of police officers, catching Toomey off-guard as there’s no financial wrongdoing occurring. Just moments later, Vendetti's car, filled with armed henchmen, crashes outside the mansion, leading to a humorous turn of events where Toomey manages to apprehend the mobsters.
Faced with the realization that his aspirations of legitimate banking are in vain, Snaps decides to revert to his old criminal ways. The film culminates in a double wedding, celebrating both Lisa and Theresa's engagements. Just as they are about to exchange vows, Oscar makes a surprise appearance, voicing his objection to Lisa's marriage, but is swiftly removed by Snaps’s men, allowing for a joyous ending.
Throughout the story, three black leather bags play a recurrent role: one filled with $50,000 cash, another containing jewelry worth the same amount, and the last is filled with the maid's (Nora's) underwear. The comedic element arises as these bags are frequently swapped among characters, leading to mounting complications for Snaps. Toomey, ever-watchful, grows increasingly convinced that the bags are filled with illicit drugs. In a twist of fate, during a police raid, it’s disclosed that the maid ends up with the jewels and cash, while Snaps is stuck with the underwear, leaving him frustrated yet somewhat relieved when Toomey finds no incriminating evidence. The movie concludes with the momentous double wedding, although it remains unanswered whether Snaps will ever reclaim his lost valuables.
