The Federation starship Enterprise, under the command of Captain Jean-Luc Picard, is en route to provide medical care for the reclusive but respected scientist Dr. Ira Graves, who lives with only his assistant, Kareen Brianon, on a remote planet. When the crew receives an emergency distress call from a nearby transport ship, Captain Picard elects to send an away team composed of Data, Counselor Troi, Lt. Worf, and Dr. Selar to see to Dr. Graves while Chief Medical Officer Dr. Pulaski stays aboard the Enterprise, which leaves to attend to the transport.
The away team finds that the request for medical assistance was made by Kareen without Graves' knowledge, and though resentful, he allows Selar to examine him. Selar determines that Graves has an incurable terminal disease and has only three weeks to live, so the team begins to collect Graves' research and records to preserve them after his death. Graves recognizes Data as Noonien Soong's creation, and claims he taught Soong everything he knew, which he asserts that if Soong is considered Data's "father" would make Graves his "grandfather". Graves and Data begin to spend significant time alone together, during which Graves reveals that he has developed a method to transfer his consciousness to a computer, allowing him to live indefinitely. Data in turn reveals that he has a shut-off switch, which he describes as his own version of death.
Later, Data reports to the away team that Graves has died. The Enterprise returns and retrieves the away team along with Kareen and Graves' body, and Graves is given a funeral ceremony. Data delivers a grandiose glowing eulogy, surprising the crew. When he later whistles "If I Only Had a Brain", echoing a habit of Graves', when entering a turbolift, Picard decides that his uncharacteristic behavior warrants an examination. Although no physical anomalies are detected, Troi's psychotronic stability tests suggest there are two personalities within Data, his original one, and one that is foreign and dominant, and threatens to replace Data's original personality entirely. Picard realizes that Graves has transferred his mind into Data; meanwhile, Graves, in Data, reveals the truth to Kareen, and while passionately proposing that she do the same so they can spend eternity together, accidentally breaks two bones in her hand due to Data's superhuman strength. Picard attempts to talk Graves into voluntarily give up Data's body, noting the harm he is causing to those he loves, but Graves knocks the captain unconscious. When Picard awakens, he and a security team find Data in his quarters. Data is back to his old self, and Kareen finds that Graves has transferred himself out of Data and into the Enterprise's computer, but only his knowledge, not his consciousness – the "human" part of Dr. Graves has been lost.
This is the first TNG episode dealing with a human mind transferred into an android. The second is the seventh season episode "Inheritance".
The title of this episode is a reference to an episode of The Prisoner also called "The Schizoid Man", as the role of Dr. Ira Graves was originally slated to be played by Patrick McGoohan, who starred in the earlier series.