The possibility of Junk is the possibility that something exists and everything is a proper part. Just as we might imagine that there are no simples—that everything has a proper part, all the way down—we might imagine that there are no caps—that everything is a proper part, all the way up. It is not obvious that this apparent possibility can be accommodated within a Lewisian modal framework. For Lewis, every possibility involves the existence of a possible world, and a possible world is just is a maximal sum, and so a cap. But the Lewisian can accommodate Junk, if she wishes, by allowing parts of possible worlds to represent complete possibilities.