The Enterprise beams up two Antedians, fishlike aliens, to transport to a conference on Pacifica. After O'Brien decides to keep the delegates, who are in stasis, "out of the way" until Pulaski takes them to sickbay, a shuttle intercepts the Enterprise, carrying another delegate: Lwaxana Troi.

Lwaxana comes on board and quickly annoys everyone. When Riker decides to carry her bags, she telepathically asks Deanna, "is he still yours?", and remarks that perhaps the custom of men being owned should be started again. She invites Picard to dinner, and he accepts, believing the entire bridge crew are invited. As he quickly discovers upon entering, however, Lwaxana intends this to be an "intimate" dinner for two.

She flirts outrageously with Picard, who manages to save himself by calling to the bridge to invite Data down for dessert, telling Lwaxana that Data's after-dinner conversation is "legendary". Data's utterly tedious anecdotes bring a quick end to the dinner, and Picard extends his gratitude to Data. Deanna, having already told Pulaski that her mother is undergoing the Betazoid version of menopause, asks her mother what she plans to do, only to hear that she plans to marry Picard! Deanna explains to Picard that Lwaxana's sex drive has gone up by at least a factor of four with the onset of "the phase", and tells him of her mother's plans. Picard, sensibly, puts Riker in command of the bridge, and runs to hide on the holodeck as Dixon Hill.

After settling in and dismissing various scenarios as too violent, Picard invites Hill's secretary Madeline to Rex's Bar for a drink. Meanwhile, when she can't find Picard, Lwaxana adopts her alternate plan, and announces her betrothal to Riker. Riker, also not surprisingly, flees with Data to the same holodeck to tell Picard about this development (and the revival of the Antedians). Picard is unpleasantly surprised to hear this, but Rex, the holographic bartender, thinks Riker has all the luck in the world.

Lwaxana, using the Enterprise computer, finds Picard and Riker, but is quickly taken with Rex, since she cannot read his mind. She decides to marry Rex, but as they reach Pacifica, Picard tells Lwaxana Rex doesn't exist. As Lwaxana leaves, husbandless, she saves the conference by revealing the Antedians are assassins.