Act I
At the Bruckner Clinic in New York City, psychiatrist Mark Bruckner is demonstrating hypnosis to his students, but a member of the audience, Daisy Gamble, proves more susceptible than the subject at hand. After class, Daisy asks the doctor if he might be able to help her stop smoking through hypnosis; she's afraid her addiction will hurt the promising career of her fiancé, Warren. During their conversation, Daisy reveals to Mark her powers of extrasensory perception: she knows when a phone is going to ring or when someone is about to drop in. She can even make flowers grow by talking to them - Hurry! It's Lovely Up Here.

Mark puts Daisy into a trance, during which Daisy reverts to what appears to be a previous life: she becomes Melinda Welles of 18th-century England. We see Melinda rejecting assorted suitors (Tosy And Cosh) and falling for portrait painter Edward Moncrief before Daisy awakes. Mark does not tell Daisy what she has revealed to him, but he does tell her that her E.S.P. is nothing to be ashamed of - On A Clear Day.

On the rooftop of her apartment, Daisy, who forgot about her date with Warren, tells some friends of the adventure she had with Dr. Bruckner - On the S.S. Bernard Cohn. Back at the doctor's office, the hypnotized Daisy travels back to the salacious Hellrakers' Club in London where Melinda first met Edward when he rescued her from the clutches of another - Don't Tamper With My Sister. Melinda finds herself unable to resist Edward, who gradually succumbs to her charms - She Wasn't You. They marry, but the artist husband finds himself unable to resist making love to his subjects.

Mark finds present-day Daisy "an aspiring conformist," but finds Melinda irresistible. And he is now convinced that Daisy's story is not a fabrication and that Daisy, who only wants to be like everybody else, is the reincarnation of free-spirit Melinda - Melinda. In a trance again, Daisy travels back to the night Melinda walked out on Edward and sailed for Boston. But the good ship Trelawney was not destined ever to reach its destination. Mark tries to save Melinda from her fate, but before he can, Daisy wakes up.

Act II
Without revealing the identity of his subject, Mark has reported his experiences with Daisy to his fellow psychiatrists, who ridicule his findings. Learning of Dr. Bruckner's belief in reincarnation, Greek shipping magnate Themistocles Kriakos arrives at the clinic. Kriakos offers to finance an investigation of the events of Melinda's life if Mark will help him find out who he's going to be in the next life so that he can leave his fortune to his future self - When I'm Being Born Again.

Alone in the office, Daisy accidentally learns that she is the woman with a past life, and that Mark prefers Melinda to Daisy - What Did I Have That I Don't Have? On the rooftop, Warren outlines to Daisy the secure future he envisions for them - Wait Till We're Sixty-Five. When Mark arrives, Daisy tells him she's "through being a go-between for you and your dream girl. You're not going to go on using my head for a motel."

At his office, Mark attempts to bring Daisy back to him through extrasensory control (Come Back To Me), and finally succeeds. He tells her he's now comfortable with her two existences, but Daisy cannot accept them, and leaves.

At the airport, Daisy's powers warn her that the plane she's about to get on will crash. Then she learns the name of the aircraft: the Trelawney. Daisy's premonition turns out to be correct: the flight is cancelled due to technical problems. Daisy finally acknowledges that she may have lived before. She and Mark go off to explore the possibilities of a phenomenal future together