A cardinality argument against five-dimensional universalism

Five-dimensional universalism (hereby stipulated) holds that if f is a partially defined mapping f from worlds to regions such that (a) if f(w) is defined, then f(w) is a nonempty region of w's spacetime and (b) f(w) is nonempty for some w, there is an object O_f that exists in every world w for which f(w) is defined and occupies precisely f(w) at w. We will call a function f with the above properties a "modal profile", indeed the modal profile of O_f.

I think that to do justice to the vast flexibility of our language about artifacts, if we want to be realists about artifacts, we will need to be five-dimensional universalists. Mere four-dimensionalism mereological universalism is insufficient, because there can be always coincident artifacts with different modal properties.

But:

1. There is a set of all actual concrete objects.
2. There is no set of all modal profiles.
3. If there is no set of all modal profiles and five-dimensional universalism is true, there is no set of all actual concrete objects.
4. So, five-dimensional universalism is not true.

The argument for (2) is that there are way too many possible worlds with spacetimes to make up a set[note 1], and for each such world w there is a different modal profile[note 2], so there is no set of all modal profiles.