At the beginning of the fourth season, Howard borrows a robotic arm and uses it to for a massage at home and then to masturbate. Due to executing the wrong program he gets his genitals stuck in the arm and has to call Leonard and Raj for help. Meanwhile, Penny comes to know of Sheldon’s new friend, Amy Farrah Fowler (Mayim Bialik), when Sheldon reads out loud her text message. To everyone’s surprise, Sheldon announces his plans to conceive a child with Amy via in vitro fertilisation with Penny being the surrogate mother. Penny suggests that he should first go out with Amy on a date. Since Sheldon cannot drive, and because the date was Penny’s idea, she is forced into giving Sheldon a ride and ends up chaperoning.
Sheldon builds a robotic replication of himself which he calls a “Mobile Virtual Presence Device” that would go through all the hazards of life that Sheldon would otherwise have to endure, while he stays behind in a “secure, undisclosed location” (his bedroom). Sheldon and Amy are very compatible with each other, as evidenced by how well they can play “counter-factuals”, a game they invented requiring them to know what the other is thinking when answering a question about “an alternate world that differs from ours in one key aspect” (Leonard flunks miserably when he attempts to play this game). However, Amy’s presence does not go down well with the other guys, who already find it difficult to handle Sheldon by himself, and they start hanging out at Penny’s apartment to escape “ShAmy” (the name the guys gave for the couple). However one day at lunch, Amy belittles Sheldon’s occupation as a theoretical physicist relative to, in her opinion, her more superior occupation of neurobiologist, prompting Sheldon to terminate their friendship. Following the breakup (or according to Sheldon, “our friendship outlived its utility), Sheldon adopts 25 cats as a substitute for Amy. It takes Sheldon’s mother to use reverse psychology to get him to reconcile with Amy.
When Amy asks Sheldon to meet her mother, he becomes worried she wants to be his girlfriend, and embarks on a series of attempts to avoid her. She eventually tells him that she only wishes to please her mother, who wishes Amy to socialize. Meanwhile, Leonard, frustrated by the fact that he is the only one of the men without a girlfriend, invokes the “Girlfriend Pact” with Howard, last mentioned in “The Creepy Candy Coating Corollary” from Season 3. Howard gets Bernadette to set Leonard up on a date with Joy, one of her friends, whose obnoxious, inappropriate behavior makes for a horrible date for Leonard. Nonetheless, Leonard agrees to another date with Joy because he may get to have sex with her. Raj’s sister Priya visits and re-ignites a heretofore unrevealed past romance with Leonard, despite Leonard’s pact with Howard years earlier that they would not try to date her in deference to Raj. When Sheldon discovers Priya leaving Leonard’s bedroom one morning, he finds out that Leonard and Priya had sex and tries to devise an elaborate, flawless lie to cover it up, but Leonard’s inability to maintain the lie results in his blurting out the truth to Raj, in turn setting off a chain reaction in which each of the four men reveal heretofore unrevealed inappropriate behavior that each has concealed from another man in the group. Wil Wheaton returns and the 4 dudes have an altercation with him outside a theatre.
Penny gets Leonard to act as her boyfriend when her father visits. When an intoxicated Raj complains that “no girl ever wants to kiss him,” Bernadette shows sympathy for him and he attempts to kiss her. In a slow motion scene, Howard stops Raj from kissing his girlfriend, however ends up to be the one being kissed. Penny gets back with her ex Zack and they all dress up as superhero to go to a comic book store new year’s eve party. Sheldon is kicked out by the remaining 3 as he dominates the creation of a new app and plays his theremin as a lament. Amy asks Penny to join her, Bernardette and the other guys on a trip to a science conference in Big Sur, California, as she believes them to be best friends. Raj develops a crush on Bernadette after she calls him a “hottie” and starts fantasizing about her. After two daydreams in which a departing Howard (once leaving to work at a university in Israel for two years, and once dying after being hit by a truck) tells Raj to take care of Bernadette sexually, he decides that he’s “definitely not gay”. In Raj’s last daydream, he and Bernadette perform a Bollywood style dance number, and he says that, dance number aside, he’s still very much not gay.
Leonard sleep with an older benefactor for funds for the university. Leonard & Priya later become a couple and stat hanging out at Raj’s apartment more, upsetting Sheldon who briefly attempts to get his own group going. Priya tells Leonard that she is uncomfortable with having Penny around her boyfriend every day. Penny spreads a rumor that Bernadette is thinking of breaking up with Howard. After the rumor finally reaches Priya, she informs Leonard that Raj has a crush on Bernadette and even writes poems about her. When Raj hears the rumor from Priya, he gets excited, as he could finally have his own shot with Bernadette. Howard is completely unaware of all this and plans to ask Bernadette to marry him. The others try to stop him from asking, as they believe that he will be blindsided when Bernadette rejects him, with Raj being the only one that selfishly encourages Howard to go through with his plan. When having dinner one night, Howard pulls out the proposal ring, as he can’t imagine a better time to ask her than with all of his friends around. Despite the protest of the others, he gets on his knees and starts to talk. At that moment, Bernadette cuts him off in what appears to be a rejection, however she actually accepts his marriage proposal, completely devastating Raj at the same time. Sheldon and Priya later clash over changes she has made to Leonard’s & the gang’s routine.
A lonely Raj decides to take an experimental drug to overcome his shyness in speaking to women. Mrs. Wolowitz is taken to the hospital after a bout a food poisoning which Howard thought was a heart attack when he told her that he was going to marry Bernadette. It turns out that Howard’s mother actually likes Bernadette a lot. Meanwhile, Leonard’s and Priya’s noisy sexual encounters sends Raj to spend the night at Sheldon’s apartment. When Leonard finds him in his bed, he proposes that Raj moves in with Sheldon until Priya finds her own place. Penny stops by, stays for dinner and the both of them get drunk from the wine Raj served. Penny tells Raj that she “screwed up”, as she shouldn’t have broken up with Leonard, and that she would be “on” him (Raj) if they weren’t friends. Priya receives a video call, Leonard overhears that she is moving back to India and storms out revealing their relationship to her parents. At the end of the episode, Sheldon discovers Leonard sleeping on their couch, Penny wakes up and is horrified when she notices Raj in Leonard’s bed beside her. She tells him that last night never happened and tries to sneak out of the apartment; however, they are busted by the others. Penny just states that “it’s not what it looks like” and leave Sheldon, Leonard and Howard confused. Sheldon inquires “What does it look like?”