<p>In ontology, parity arguments hold that because we allow some kind of thing in our ontology, such as snowballs, then for reasons of parity, we should add some similar kind to our ontology, such as a snowcubes, and we should move toward unrestricted composition or modal plenitude. I argue that current parity arguments do not succeed, and I present two challenges for future parity arguments. First, the anchoring objects for parity arguments, such as snowballs, are disproportionately kinds of things that are mind-dependent insofar as the kinds would not exist without mental work. These mind-dependent existence conditions have flown under the radar. If we begin a parity argument with something whose existence is mind-dependent, then we can expand the ontology only with other mind-dependent kinds. With this constraint, we are far from establishing unrestricted composition. So the first challenge is to develop parity arguments that can fill out the ontology with mind-independent kinds. Second, ontologists should anchor parity arguments with more-certain existence claims. For example, the existence of the kind <i>tortoise</i> is more certain than the existence of the kind <i>islands</i>. I argue that there is room for growth in starting with a solid existence claim. By using more-certain existence claims, we increase the strength of the argument and better motivate a conclusion that adds to the ontology rather than subtracts.</p>