Although Fuller House focuses on D.J., Stephanie, and Kimmy as adults, characters from the original series guest star all the time and even have storylines. For instance, Jesse and Becky adopted a baby girl in Fuller House Season 2 over the course of several episodes. The plotline begins in the episode "Fuller Thanksgiving," in which the Tanner, Fuller, and Gibbler families get together for the holiday. Becky and Jesse arrive at the gathering while fighting, and the audience finds out the subject of their argument when they're alone: Becky wants to adopt a baby, but Jesse doesn't.
"I'm serious, I have baby fever," she tells Jesse when they're alone in their old living quarters of the Tanner house. He's not as enthusiastic about adding another child to their brood, which already contains their grown children, twins Nicky and Alex. "Becky, as you know, I'm a man of a certain... age," Jesse tells Becky. "If we adopt a kid now, by the time it's in junior high school, I'll be on my third hip." Becky reveals that she misses those "parenting moments," which she doesn't have as often with their now-adult offspring, but Jesse confesses that he enjoys his time alone with Becky. They try to compromise, to no avail. Later, the spat intensifies enough that Becky kicks him out of their room.
During the taking of the family photo, Becky coos over D.J.'s baby Tommy Jr. and asks Jesse, "Don't you want to adopt one of these?" This leads the whole family to think Jesse and Becky are adopting, but Jesse gets booed when he shuts down the celebration. Later in the episode, Stephanie gets Jesse to bond with Tommy Jr. by reading him a bedtime story in an effort to get him to consider Becky's side. Becky walks in on Jesse's story and tells him that it's OK if he doesn't want to adopt a baby. "Jess, I didn't just want to raise another child, I wanted to raise one with you," she explains to him, adding that she wants them to be all-in if they are going to grow their family. At dinner, Jesse finally comes around and announces that he too wants to adopt a baby with Becky and they celebrate their decision.
In the episode "Glazed and Confused," Becky and Jesse meet with Mrs. Lopez, a representative from an adoption agency on the set of Wake Up USA. After Jesse doesn't make the best first impression on her, he tries to make it up to Mrs. Lopez by taking her to the set of the fictional TV show Police Mom. Of course, the plan seems to be working — it's Mrs. Lopez's favorite TV show —until the gang gets stuck in the set's jail cell. Mrs. Lopez overhears Jesse give a pep talk to Stephanie and she's so impressed. It prompts her to give them the recommendation they need for the adoption.
Jesse and Becky meet their new child at the end of the New Year's episode, "Happy New Year Baby." Jesse introduces the baby girl to the family and announces her name: Pamela. This is a significant name for the Tanner family: it's the name of Jesse's late sister, who was Danny's wife and the mom of D.J. and Stephanie; the first Pamela passed away before the original Full House premiered in 1987. Fuller House Season 2 ends as the family coos over the newest Katsopolis.
Now that Baby Pamela has joined the Fuller House brood, surely the adorable infant will get into plenty of hijinks with Jesse, Becky, and the rest of the family in Season 3 and beyond.