I figure that the AI would most likely create a copy of itself, modify that, and see how it turns out.
Start making many copies and self-directed evolution starts to compete with evolution via natural selection.
I was thinking it would stop running the old copy if the new one works out.
Peter Suber is the Director of the Harvard Open Access Project, a Senior Researcher at SPARC (not CFAR's SPARC), a Research Professor of Philosophy at Earlham College, and more. He also created Nomic, the game in which you "move" by changing the rules, and wrote the original essay on logical rudeness.
In "Saving Machines From Themselves: The Ethics of Deep Self-Modification" (2002), Suber examines the ethics of self-modifying machines, sometimes quite eloquently: