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In San Francisco, classical violinist Roger Grant performs at a society Nob Hill string quartet recital.  Roger's Aunt Sophie and his teacher, Professor Heinrich, predict he will be a great musician.  Following the recital, Roger goes with three other musicians, pianist Charlie Dwyer, drummer Davey Lane and Louis, a clarinetist, to audition at "Dirty Eddie's," a Barbary Coast saloon, which is looking for a band.

Upon discovering that their music is missing, the bartender, Bill Mulligan, gives them sheet music that was left on the bar by prospective singer Stella Kirby, which she received from a friend in New York.  Stella has raved that nothing like the piece, which has an unusual time and rhythm, has been heard on the Barbary Coast before.  When she hears the song, Stella, thinking that the band stole it, joins them and sings.  The song, "Alexander's Ragtime Band," written by Irving Berlin, greatly pleases the patrons and owner, who hires the band and Stella, and dubs Roger "Alexander."  Although Stella is still miffed, Charlie convinces her to remain with the band.  Roger, adopting his new name, fulfills his desire to have his own band, which grows in size, but Aunt Sophie and Professor Heinrich are disappointed in him.

As the band plays in increasingly classy places, Roger, who says he wants to set the world on fire, constantly quarrels with Stella, who only wants a job, and Charlie acts as conciliator.  Before the opening of the exclusive Cliff House, Charlie plays a romantic song for Stella, which he wrote for her, and as she sings it during the performance, she and Roger, in a glance, realize that they love one another, which Charlie painfully sees.

When Charles Dillingham, a top New York producer, asks Stella to come to New York, where, he says, he can make her a star, Roger, rather than joining Stella's and Charlie's delight, argues against the move.  After Roger orders Stella to leave, Charlie, who philosophically accepted his friends' romance, quits also.

During World War I, Roger and Davey convince a colonel to allow them to put together a show to run on Broadway to rival a Navy revue.  Stella tries to visit Roger backstage, but he refuses to see her; when a transport order interrupts the show and he marches with the others to the docks, she cries.  After the war, Roger visits Stella, now a star, during a rehearsal and, after asking her forgiveness and confessing that he has never stopped loving her, learns that she and Charlie have been married for more than a year.  Depressed, Roger joins Davey and singer Jerry Allen in a new band.

One year later, Charlie and Stella run into Bill Mulligan, now a bootlegger, and learn that Roger is playing in Greenwich Village.  Realizing that Stella still loves Roger, Charlie proposes an amicable divorce.  Stella goes to the club and, although she and Roger exchange loving glances, when she learns that Jerry was responsible for getting him out of his depression and that the band is sailing for Europe the next day, she refrains from approaching him.

While in Chicago on tour, Stella quits and disappears.  In London, Roger proposes to Jerry, but knowing that he does not love her, she turns him down.  When Roger returns to New York and auditions songwriters for his new radio program, Charlie comes and reveals the divorce and tells Roger that Stella still loves him.

Stella, who has been performing in cabarets under an assumed name, arrives in New York just as Roger's Carnegie Hall swing concert, which Aunt Sophie and Professor Heinrich proudly attend, is about to begin.  Stella finds Bill, now in his own restaurant, but refuses to accompany him to the hall.  While Bill secretly arranges for Roger to meet Stella after the show, she leaves the restaurant and takes a taxi through the park listening to the concert on the radio.  When the driver pulls up outside Carnegie Hall, Stella attempts to purchase a ticket, but learns that the show is sold out.  The taxi driver invites her back to hear the rest of the concert, but as Roger is about to introduce "Alexander's Ragtime Band" as his encore, she cries and requests the driver to turn the radio off.  He refuses and, after she hears Roger say that he is playing the song for the one person with whom he associates it, the driver reveals that he knew her identity all along.  Emotionally overcome, Stella goes backstage.  Bill finds her and brings her to the wings, where Charlie notices her and attracts Roger's attention.  He embraces her and brings her on stage, where she joins the band in the song.