Here’s a curious thing: an unchanging object can have one shape at one time and a different shape at a different time.
Example 1: In the context of special relativity, times are spacelike hyperplanes. Suppose a special relativistic universe, and suppose that an object is an unchanging cube. Well, being a cube is not invariant between reference frames. So there will be one reference frame F1 at which the object is an unchanging cube and another reference frame F2 where it has some other unchanging shape. Each reference frame defines a family of times, i.e., spacelike hyperplanes. At the times of F1, the object is cubical and at the times of F2, the object is not cubical. Hence, at one time the object has one shape and at another it has another.
One might think that this example can be handled as follows: the object unchangingly is a cube-relative-to-F1 and a non-cube-relative-to-F2, and it is a cube-relative-to-F1 even at the times of F2 and a non-cube-relative-to-F2 even at the times of F1. But that’s probably mistaken. It seems to make no sense to talk of the shape-relative-to-F1 at times in F2. So we still have a difference in relative shape: the shape-relative-to-F1 is well-defined at F1 times but not well-defined at F2 times.
Example 2: Different universes will have different spacetimes, and hence different times. Suppose an object that is wholly present simultaneously in multiple universes—after all, that seems no harder than multilocation within the universe, and we have some evidence of miracles where a saint is in more than one place at the same time (for an account of such possibilities, see this). In each universe the object is unchanging, but it has a different shape in different universes. Since the different universes come with different times, the object has one shape at one time and a different shape at a different time.
This seems to be a refutation of the at-at theory of change, on which change just is difference in properties across times. But while the cases, if possible, do indeed refute that theory, there is a slightly richer at-at theory that is unaffected by them:
an object changes from having P to having Q provided that it has P and not Q at an earlier time and has Q and not P at a later time
an object changes with respect to having a property P provided that it changes from having P to not having P or from having not-P to having P.
So it’s easy to fix the at-at theory. Still, I think something has been learned here: there is an essential directionality to change.