An alien vessel in need of rescue suddenly appears in Voyager's space. It is attempting to use an experimental propulsion system powered by a coaxial warp drive, but it is destabilizing. Janeway transports the pilot, Steth, and his prototype to Voyager. Paris, who has been restless and irritable lately and in need of a change in duty, volunteers to help him repair his ship. What they don't know is that there is really a woman inside Steth's body.

While Paris uses his knowledge of 20th-century cars to repair the ship, Steth breaks into Voyager's computer and downloads Paris' DNA information. Once Steth's ship is operational again, he suddenly overtakes Paris and switches bodies with him. Steth sends Paris away on his ship, and he stays on Voyager to live out Paris' life.

Steth slides right into Paris' daily routine, and the crew is none the wiser. He uses flattery with the Doctor to get out of sickbay duty, and he charms his way back into Torres' good graces to smooth over a recent fight she had with Paris. Meanwhile, Paris wakes up on Steth's ship to find that the Benthan, who have tracked down Steth for theft, are taking him into custody.

The Benthan ships are suddenly run off, and an angry woman, Daelen, beams aboard Paris' vessel. She says she is Steth, and she wants her body back. On Voyager, Steth begins to lose control and exhibit erratic behavior. He fights with Torres and Seven of Nine, and he becomes intoxicated while on duty. When Janeway expresses her concern, Steth attacks her and is taken to sickbay after Tuvok stuns him with a phaser.

Daelen explains that the alien has perfected selective DNA exchange. It put Steth into its body, and Paris into Steth's. They finally activate the coaxial warp drive and manage to catch up with Voyager, but when they tell Janeway what has happened, they realize the alien has switched bodies again. Janeway is lying in sickbay in Paris' body, and the alien in her body takes off from Voyager in a shuttle it has outfitted with the advanced propulsion system. Paris and Steth race after her, and Paris applies the principles he used in repairing the warp drive to disable it. With the alien in custody, everyone is returned to the proper bodies, and Paris has gained a new appreciation for the monotony of his life.