For example, when a young troubled child progresses from torturing insects with a magnifying glass to killing small mammals, or when a stalker changes their behavior from just following someone around to breaking into their house, etc.
It usually involves the new behavior being more risky for the assailant, more harmful for the victim, and more illegal/immoral.
Edit: I know escalate fits the definition, but I think there's another word that has a criminal/immoral connotation that I am looking for. Some other synonyms to the word I'm looking for might be spiral (downward), descend, or intensify.
By request, some sentences for you to fill in the blank:
John used to just stare creepily at his classmate, Jane, all throughout English 101 but today his behavior _______ and he gave into the urge to follow her back to her dormitory after class.