 Though free from some difficulties inherent in Lewis’s theoretical machinery, modal–dimensionalism has its own obstacles to overcome, not the least of which is to make substantive sense of the idea of an object’s persisting not just in physical space and time but in modal space. One idea is to mimic the “endurantist” approach to temporal persistence and say that a possible object persists through many possible worlds by having all of its parts existing at each of those worlds. Another idea is to mimic the “perdurantist” approach to temporal persistence and say that a possible object persists through many possible worlds by having different parts (world stages) at different possible worlds and being the modal-dimensional “worm” consisting of those world stages. Note that this does not make the object mereological part of a possible world at which it exists. It only makes each of the object’s world stages part of the object. Lewis, in contrast, has it that a possible object has all of its parts at a single possible world (where they are mereological part of that world) and therefore does not persist through different worlds at all. Despite these differences, Lewis, speaking of the “perdurantist” version of modal–dimensionalism, says that it is but a notational variant of his own theory. He then proceeds to criticize it (Lewis 1968: 40–2). Lewis formulates his opposition to modal–dimensionalism more carefully in Lewis 1986: 213–20. Achille Varzi derives Lewis’s theory from a theory similar to modal–dimensionalism (Varzi 2001). Unlike modal–dimensionalism, the theory he uses follows Lewis and defines the existence of a possible object at a possible world in terms of the object being mereological part of the world. Varzi notes some differences between this theory and Lewis’s. Vacek 2017 defends modal-dimensionalism from some objections.