Martin dreams in 2D: in form but not in substance. By changing her famous brownies to low fat, Mrs. Brown inadvertently changes Martin's constitution as Martians are affected by polyunsaturates; basically she has poisoned him. So his dreams change from being 2D to 3D, and they also don't go away.

Martin uses his memory-wiping machine on Tim, which causes him to fear his "Uncle" and out him as a Martian to Mrs. Brown and the authorities, so Martin wipes Mrs. Brown's memory, then his very own.

Martin creates a neuro cerebral stimulator to help him make up his mind about whether to go home in an unmanned rocket, or continue to stay on Earth with his new family, Tim. A lightning strike to the stimulator causes Martin to split into three: two decisive Martins on either extreme and an indecisive Martin. Once all three Martins come to a consensus on any issue, they will rejoin. Can they agree on anything?

Dulcy, Henry and Stanley - Mrs. Browns' sister and her husband and son - come for a visit. Henry is a computer hardware expert and as such believes that everything has a scientific explanation. Stanley is a typical boy with a vivid imagination, which Henry, with a heavy hand, tries to suppress. Stanley sees Martin's spaceship entering the garage, which he wildly exclaims to his father, who chastises him for making up lies.

While fixing Mrs. Brown's TV antenna, Tim accidentally cuts a live telephone wire which hits Martin, in turn turning him into a live telephone. Martin has to figure out how to disconnect himself back to normal before Mrs. Brown and Det. Brennan (who was called in to find Mrs. Brown's pocketbook) stop buying their explanations for the telephone ringing and mysterious voices. But before he does, Martin and Tim overhear on Martin's telephone a plot to steal the Vandeleer diamond.

Tim is writing a series on ESP. When he unavoidably brings the professor, the subject of his story, to the apartment, Martin hides his ESP so he can't read his thoughts. In the process, Mrs. Brown gets his ESP and regresses to a toddler.

To earn some money, Martin decides to tutor, his first student being precocious 12-year old Eddie Prescott, the son of a seemingly tough-as-nails air force captain who wants his son to enter into the prestigious air force academy. Eddie's tough exterior masks insecurities of stupidity. During Martin and Eddie's first lesson, disaster strikes because of Eddie's silver braces; Martians are rendered brain dysfunctional when exposed to pure silver. As Eddie begins to learn, Martin begins to forget.

Martin creates a replicating machine, the duplicates from which only have a limited lifespan. Tim accidentally duplicates Mrs. Brown and Det. Brennan takes out the duplicate on a date. At the restaurant, a second Det. Brennan is produced.

Martin finds out that Mrs. Brown is in financial straits due to her over generous nature. Through noodle soup, Martin gives her some Martian subliminal messages to save money, the suggestions which have an extreme effect. She no longer trusts banks so she withdraws all her money and keeps it at home, and she kicks Tim and Martin out of the apartment for being late on their rent. But there's a bigger problem: there's a friendly neighborhood cat-burglar, and Mrs. Brown now has a houseful of cash.