Is there more than one categorical property?

I develop a new theory of properties by considering two central arguments in the debate whether properties are dispositional or categorical. The first claims that objects must possess categorical properties in order to be distinct from empty space. The second argument, however, points out several untoward consequences of positing categorical properties. I explore these arguments and argue that despite appearances, their conclusions need not be in conflict with one another. In particular, we can view the second argument as supporting only the claim that there is not a plurality of categorical properties, and not the stronger claim that there are no categorical properties whatsoever. I then develop a new account of properties which capitalizes on this insight.