Damian who runs a restaurant in Taipei and has always had a dream of "getting a family and raising children". After two years of stable relationship with his boyfriend Jie Li, the two embarked on a surrogacy journey together and successfully gave birth to his son Kai Kai. Until the son entered the kindergarten and began to face the curiosity and differences of his peers and the gossip of the parents, the two fathers had to think about how to explain to the young Kaikai what "mother" was.

Following the events at the end of season one, the family of Jerry, Damian and their four year old son, Kai, now have an additional, uninvited guest––Jimmy, Damian’s son from his previous marriage in California, whose unexpected arrival to Taiwan brings much turbulence to the otherwise peaceful family. Damian’s gentleness towards his ex-wife Kate as well as his love for Jimmy fills doubts in Jerry’s heart, fearing that the bisexual Damian might revert to liking girls. Elsewhere, Jerry is also having to deal with his persistent mother, who is constantly pressuring him to make his own baby. Meanwhile, Damian, on the other hand, finds himself in a predicament between taking care of Jimmy and facing Jerry. Season two of Papa & Daddy focuses on the intricate dynamics between queer couples and their families. Straight or gay, managing a long-lasting relationship will always require wisdom.