Time-Indexed Relations
I don't share Lewis's strong intuitions that shape properties must be purely intrinsic rather than time-indexed. For me, the argument from intrinsic change works much better with certain relations, in particular mereological relations and identity.
Suppose x is part of y at time t1, but not at t2. Perdurantists can say that the temporal part of x at t1 is a part simpliciter of the temporal part of y at t1. Time-indexers will say that the whole of x stands in the part-at-t1 relation to the whole of y, where this relation is not analysable in terms of non-indexed parthood: time-indexed parthood is all there is. But no! Subsets are parts simpliciter of sets, battles are parts simpliciter of wars, the story of the Trojan War is a part simpliciter of the Illiad, geometry is a part simpliciter of mathematics, XPath is a part simpliciter of XSLT, and so on. These things are not part-at-time-related, but part-related.
Similarly for identity: Suppose x is identical to y at t1, but not at t2. But identity is not a time-indexed relation. Lots of things are identical simpliciter to themselves.
(Why should one believe that things are identical only at certain times? To solve the paradoxes of coincidence. A statue and a piece of clay are identical at times when the clay constitutes the statue. There are of course alternative solutions to the paradoxes, but they all seem much worse to me. I wonder why so few endurantists adopt the simple time-indexed identity solution, suggested by Lewis in "Against structural universals", and rather go for crazy solutions like mereological nihilism or essentialism.)