One reason to believe in mereological universalism is that mereological universalism lets one's ontology include artifacts tables and chairs, without the weird consequence that what entities exist depends on what people have thought. For given any bunch of parts, there is a possible world where that bunch of parts was thus placed by a person with a unified purpose, and hence that bunch of parts is an artifact. But whether that bunch of parts thusly arranged is an object should not depend on what went on in the mind of that person. So, either the bunch of parts is an object in both the world where it is an artifact and the world where it is not, or it exists in neither world. Therefore, if artifacts exists, mereological universalism is true.
Here are some problems for this combined view—the view that accepts mereological universalism as a way of making sense of artifacts.
1. Hermes in the stone: In our world, the sculptor has made the marble statue of Hermes; in w2, he hasn't, and there is just the block of marble. But if our world's Hermes is identified with a mereological sum of bits of marble, he exists in w2 as well. (Moreover, he exists in our world even before he was sculpted—this consequence can be avoided by an appropriate four-dimensionalist move.) It is not the case that the artist has caused the Hermes to come into existence. So the approach only does justice to some of our intuitions about artifacts. (This problem can be eliminated by supposing a five-dimensional mereological universalism, where the "fifth-dimension" is worlds.)
2. suppose now that our most fundamental ontology does not include bits of matter. Instead, what we have are fields. It now is no longer clear that mereological universalism by itself yields the existence of artifacts. One might try to generalize mereological universalism to the situation by letting the parts be something field-points, where a field-point can be represented by a triple <x,F,v> where x is a spacetime point, F is a field type (e.g., electromagnetic), and v is the actual value that F has at x. Artifacts then would be four-dimensional mereological sums of field-points. But do field-points really exist? The abstract triples that represent them maybe do, but the field-points themselves are not identical with the triples because the triples are necessary beings, and hence so would their mereological sums be. Moreover, which field-points get included in the chair? This, I guess, is a species of a standard boundary problem like the one Unger uses to argue for his non-existence, but it seems to me even more problematic in the field setting. Suppose, for instance, that on a particle model the object's particles would have some wave-functions. The wave-functions may well be non-zero everywhere in space, though their values are very small outside a small region. So it seems that there is a sense in which an ordinary object should be thought of as existing almost everywhere in some sense, but particularly concentrated in some area. But the field-point-sum object can't exist everywhere, even if the associated wavefunctions are everywhere non-zero, because then there would only be one field-point-sum object—the one consisting of all the field-points there are—and all artifacts would be the same.