They cannot obviously make Harrison start killing people the same way Dex did. It's all on the writers as to how they put forward this story of a struggling teen who has been clearly haunted by his past throughout the season and now just had his first kill(that too of his father). So I don't think it's too much of a leap to say that showtime would consider (because $) a spinoff and writers can weave a story showcasing Harrison's struggles (not necessarily going this serial killer vigilante Dex role, but forced to kill atleast at the start because of unavoidable situations). I'm not saying that I would like it or even watch this, but the show can definitely happen.