Set-theoretic potentialism is the view that the universe of sets is potentially infinite: it can always, necessarily, be expanded to a more inclusive universe of sets. One version of this view is that the set-theoretic universe can always be expanded to a forcing extension in particular. This view has primarily been studied from a technical point of view, however; in this chapter I explore what philosophical conceptions of set theory might motivate forcing potentialism. I begin by raising an explanatory challenge for any form of width potentialism based on the iterative conception of set and then sharpen this challenge to argue that any broadly iterative conception of set is inconsistent with the claim that the possible width extension of a universe are exactly its forcing extensions. Finally, I suggest one possible way meeting the explanatory challenge by disentangling the iterative conception of set formation from the combinatorial conception of sethood. This makes room for what I call the iterative logical conception of set. I sketch a toy model of a potentialist system which is both height- and width potentialist and where the width extension include all (but not only) the forcing extensions.