Vicki and the Solomons continue to search for Harry, who was abducted and sold to a circus by Vicki's ex, Randy, where Harry's transmissions from The Big Giant Head award him popularity as the act "Hargo the Alien". Meanwhile, the loss of Harry means that the aliens' status report continues to remain past-due, for which The Big Giant Head's punishment is to slowly cease Dick's brain functions. The group races to find and convince Harry to transmit their report and come home to the family and Rutherford before it is too late for Dick.

The Solomons discover a brand of new collectibles called Fuzzy Buddies (a parody of Beanie Babies) when eating at a fast food diner, and Dick soon becomes so obsessed with collecting them that he begins to lose control of his family's finances. Tommy's coach is annoyed at his lack of team 'pep' and so makes him the school mascot - a giant owl called Hootie. Things goes wrong, however, when Tommy becomes so high on school pep that he attacks the coach.

Dick is annoyed that Mary, in her new position as Dean, has little time for him anymore, and is even more annoyed when he is told that he has to share is office with new literature professor Jennifer Ravelli (Laurie Metcalf). Despite his initial dislike, and attempts to stay loyal to Mary, he soon becomes infatuated with Jennifer. Sally tries to fix Nina up with Don's cop friend Eric, but becomes irritated when they don't take to each other. At Happy Doug's bar, Tommy fixes up an old 'love tester' machine but is disappointed when it classifies him as 'cold fish' and Harry 'hot stuff'.

On his way to his first dinner-date with Jennifer, Dick suggests to Mary that they should see other people, who laughingly agrees, assuming it to be a cry for attention and doubtful that another woman would have him. Dick's so-called love for Jennifer quickly wanes, as her initially charming quirks become annoying, and he begins to miss Mary. Meanwhile, Sally, Harry and Tommy experiment with the traditional purposes of various rooms at home, rearranging furniture and appliances.

When Playpen magazine arrives at Pendleton, looking for students to pose nude, Sally decides to take part. While Dick encourages this, Don is furious. Dick is horrified when he discovers that Mary posed nude for an art shoot twenty years ago, and tracks down the photographer. Harry decides to test if clothes are "all a big scam" by becoming a nudist. Tommy has his eyes on his new lab partner, Alissa Strudwick (Larisa Oleynik).

An invitation arrives in the mail from an 'Aunt Florence', inviting 'Richard Solomon' to attend a Solomon family reunion in Indiana. This is obviously a mistake, so Dick phones Florence to set the record straight. Upon discovering that Richard is so estranged that his family wouldn't recognize him anyway, he decides that the aliens could do with some roots and accepts the invitation. Upon arriving, however, it becomes clear that the only reason the real Richard is estranged is because of an old family fallout - and it hasn't burned out yet.

When Harry's boss Doug starts deducting income tax from Harry's paycheck, the Solomons realize that they have never filed a tax return and that they owe $9500 to the government. To combat this, they invent the 'brilliant' notion of lying on their tax return and Dick reworks the sums so that the government owes them several hundred thousand dollars. Sally attempts to help by setting up a failed home hairdressing business, but when women start arriving for haircuts, Harry and Tommy 'camp up' and take to the 'salon' to help. Lying doesn't work, however, and the Solomons are faced with an audit - and the threat of being exposed as aliens.

When a meeting is rescheduled without her having been notified, Mary begins to have doubts about the longevity of her position as Dean, and Dick leads her to become paranoid that there is a conspiracy to have her removed from her job. The pair decide to investigate, and end up breaking into Judith's office by night for evidence, only to be caught by the police. Vicki Dubcek decides that the best thing Sally needs to help her get over her break up with Don is a weekend of riverboat gambling on the Cincinnati Queen, a floating casino - where Harry manages to win big, while Sally gets her lips on a Neil Diamond impersonator (Bryan Cranston).

Dick realizes that he doesn't know how to use a computer and strives to learn how to use one. When he does it takes over his life and he becomes a recluse. Sally and Tommy decide to do away with their old TV in favor of a newer, better one, but end up becoming addicted, wanting all the latest features. Harry and Vicki, however, are trying to get pregnant, but the medical-science part of it is turning Harry off. Guest appearance by Edward Herrmann.

Dick, Tommy, and Harry begin to notice that, since Sally moved out, their apartment has become filthy. Mary suggests that Dick hires her maid part-time, but, to her annoyance, Dick ends up stealing her full time. When Sally finds out that she has been replaced, she is hurt. Tommy has managed to get himself in charge of the school newspaper, but he becomes so dedicated to printing the absolute truth that he begin to worry school officials and even alienate his girlfriend Alissa.

Dick is jealous when fellow physics professor Vincent Strudwick publishes a critically acclaimed, bestselling book on physics, and, while Mary busies herself showing the visiting Nobel Prize winners around the campus, he decides to write a second book that will better Strudwick's. He then realizes, however, that he cannot publish all the secrets of the universe without raising unwanted questions, and so looks for another way to get at Strudwick, using Tommy and Alissa - who, it turns out, is Strudwick's daughter. Sally and Don decide to start hanging out as friends, but soon find themselves unable to resist each other.

When Sally, Harry and Tommy are nearly crushed by a chandelier in a restaurant, they feel reborn, as if they are discovering everything for the first time. Dick is jealous, however, and while Sally and Harry volunteer themselves at a homeless shelter, he strives to have a near-death experience so that he might enjoy life like they do - and a faculty trip into the mountains presents itself as the perfect opportunity. Meanwhile, Tommy decides to waste no more time in his life - and asks Alissa to marry him.