Gayla and Steve Erickson are in San Francisco to confer with a specialist about their ten-year-old son, Josh, who is dying from a rare blood disease. In preparing for a bone marrow transplant, the doctor's tests reveal that Steve is not Josh's biological father. Alice and Bill Korman arrange a blind date for their unmarried, plain friend, Millie Broome, who is in town for a teachers' conference. When the date has to cancel, Alice hires a professional escort, Charles Vandoor, who spends the night with Millie and finds himself infatuated. While Charles waits for the right moment to reveal his line of work, Millie accidentally finds out from Charles's enthusiastic former client. Receiving most of the attention at the St. Gregory Hotel, however, is the celebrated clairvoyant Constantin Markos, who is in town to perform his unique skills. Markos, an old acquaintance of Mrs. Cabot's, impresses Peter when he predicts that a redhead will soon enter his life.