In one comic strip he was seen dreaming that he was a huge t-rex chasing people.
In other strips Jason has created costumes in which he places Quincy on his head and (generally) one of Roger's large coats on and annoys his family. The costumes include Iguanoman, The Lone Iguana, Black Bart, Don Iguan, and Quincy John Adams. And of course, Quincy's Mother. Jason talks as Quincy or whoever Quincy is at the time.
Jason isn't choosy, he torments all girls with Quincy, however, his teacher, Miss O'Malley loves him.