The chairman of a large automobile maker is left to find a new second in command and narrows it to three equally qualified candidates. To make his decision, he decides to examine each of the men's wives and learn something about the candidate through their relationships.

Following the death of Philip Briggs, the general manager at luxury automobile manufacturer Gifford Motors, owner Ernest K. Gifford decides to select his successor from among the top three district managers. The snobbish Gifford orders the men to come to the company's headquarters in New York City and to bring their wives, as he believes that the wife of a man in such an important position is as valuable to the company as her husband. Arriving by plane are Bill and Katie Baxter, a devoted couple reluctant to leave their children in their Kansas City home. Jerry Talbot, traveling by train from Texas, warns his sexy wife Carol to let him handle Gifford his own way. Elizabeth and Sidney Burns, who are on the verge of separating, quarrel as they drive from Philadelphia, and Sid begs Liz not to reveal their marital problems. Liz promises to act like a dutiful wife, although she is embittered by Sid's devotion to work, which has given him an ulcer and strained their marriage. After the couples settle into the lavish hotel suites provided by Gifford, they discuss their trip, and Katie, who believes that the trip is a reward for good sales, expresses her dislike of the big city. Carol, meanwhile, reiterates her desire to leave Texas and become part of a more glamorous lifestyle, and Liz states that if Sid is promoted, he will work himself to death. After Bill warns the nervous Katie not to have more than one martini, they attend a reception hosted by Gifford, and Liz is bemused to see the glamorous Carol staging a grand entrance during which she catches Gifford's eye. Katie rapidly downs three martinis, then hiccups while Gifford makes a speech and further endangers Bill's position when she tells Gifford that she hopes he will not give Bill a job in New York. Realizing that she has made a faux pas , Katie runs off, and Liz is impressed to see that Bill pursues her rather than staying with Gifford. Back at the hotel, Jerry chastises Carol for her overt flirting and demands that she let him prove that he is the best man for the job, while Sid thanks Liz for her support. Bill finally reveals to Katie that he is being considered for Briggs's job and is saddened by her negative reaction. The next day, Gifford's nephew, Tony Andrews, takes the women sightseeing while Gifford takes the men on a tour of the company's factory. Gifford questions the men about their views on leadership, and Jerry reveals his theory of an undefinable quality that he calls "X+" that enables a man to be a productive leader. The men join their wives, and Sid excitedly tells Liz that he believes he has earned Gifford's favor. Liz replies that he is only getting closer to the end of their marriage and storms out of their room, while Carol continues to pressure Jerry about the job. Katie admits to Bill that she made several gaffes while talking with Tony, and Bill reveals that he, too, spoke his mind plainly to Gifford and is not sure how he was received. Bill asks Katie to buy some "flashier" clothes, however, in the hope that Gifford will pay attention to her, as he has been to Carol. Meanwhile, Gifford visits his sister, society matron Evelyn Andrews, and asks her to host a dinner party so that she can evaluate the wives, but Evelyn insists that she will need more than just one evening. The next day, Gifford announces to his visitors that they will be spending the weekend at his country home, and Katie, who has spent her clothing allowance on a new barbecue for Bill, is crushed to learn that he really does want the promotion and that she has therefore squandered her money. Desperate to impress Gifford, Katie asks Liz for help, and Liz takes her to a bargain basement where they find her some adequate clothes for the weekend. During the yacht ride to Gifford's estate, Sid, who has promised Liz that he will put their family life ahead of his work, assures her that his ulcer no longer hurts because he has stopped caring about the promotion. At the estate, Gifford shows the men his trophy room while Evelyn offers the women tea. Katie "accidentally" spills tea on herself in order to spend some time with Evelyn alone, and Evelyn offers her advice on the rigorous duties faced by a "company wife." In the trophy room, Gifford bluntly tells the men that he has been "inspecting" them and their wives and asks them if they will put their jobs ahead of their family lives. Bill flatly refuses, stating that if a man's work and home life interfere with each other, something is wrong with both the man and the job, while Jerry replies that he wants to be accepted on his own personal merits, not his wife's. Sid eagerly assures Gifford that he wants the general manager's post, then, upstairs, confesses to Liz that he would not be able to turn down the promotion if it were offered to him. Resigned, Liz promises to stick by him, while Katie is relieved to learn that Bill has decided he does not want the job. The scheming Carol, hearing Jerry's bitter description of Gifford's machinations, goes to Gifford's study and insinuates that if he promotes Jerry, she will become his mistress. Gifford replies that he is not giving the job to Jerry, who he says has a terrible handicap holding him back despite his talent, and when the infuriated Carol tells Jerry, he lashes out at her. Telling her that he is sick of her interference and sexual games, Jerry orders her to leave, then goes down alone to dinner. Knowing that Gifford will be announcing his decision after dinner, the couples glumly poke at their food until Evelyn upbraids her brother for being sadistic. Gifford tells Bill and Sid that the company takes pride in them, then tells Jerry that although he was the best man for the job, he had something holding him back. Realizing that Gifford is referring to Carol, Jerry is gratified when Gifford praises him for having the courage to change his life, then offers him the job of general manager. The happy guests then celebrate by joining Gifford in a toast to his team, their wives and a "great, big, wonderful woman's world."