 Let us now consider the second way of extending M mentioned at the beginning of Section 3. Just as we may want to regiment the behavior of P by means of decomposition principles that take us from a whole to its parts, we may look at composition principles that go in the opposite direction—from the parts to the whole. More generally, we may consider the idea that the domain of the theory ought to be closed under mereological operations of various sorts: not only mereological sums, but also products, differences, and more.