  The classical and medieval authors who developed DDI did not operate with an explicit classification of changes.  But Anselm, for instance, argues both that God is immutable and that His relations with other things can change (Monologion 25) and Aquinas does the same (ST Ia 9 and 13, 7). So as they understand DDI, it lets God change extrinsically. Suppose that at t, Quine begins to worship God. Then at t, God comes to have a new relational property, being-worshipped-by-Quine. This is clearly an extrinsic change, since its occurring in God implies the existence of someone “outside” God, namely Quine. God does not (let's say) do anything to cause this. It's a matter of Quine's free will. Quine doesn't do anything to God by worshiping him. And this change in God is a logical parasite of the real changes in Quine which constitute his beginning to worship God. It's not possible that becoming worshipped by Quine be the only change in a universe. Quine's beginning to worship must occur too if this one does. DDI thus lets God become Quine-worshipped. It rules out only real and intrinsic changes.