The conventionality of geometry is merely incomplete

Empiricists following Poincar\'e have argued that spacetime geometry can be freely chosen by convention, while adjusting unobservable structure so as to maintain empirical adequacy. In this article, I first strengthen a no-go result of Weatherall and Manchak against the conventionality of geometry, and then argue that any remaining conventionality arises from scientific incompleteness. To illustrate, I discuss a new kind of conventionality that is available in the presence of higher spatial dimensions, and illustrate how the incompleteness in such models can be resolved by introducing new physical theories like Kaluza-Klein theory. Conventional choices of this kind may provide a fruitful starting point in the search for new science, but if successful would eliminate the conventionalist alternatives.