Boris Kment formulates two challenges to anti-haecceitism: one based on the concept of chance, and the other involving counterfactuals. In this paper I refute the chance-based argument by appropriately reformulating its premises in a non-individualistic language. Regarding the argument from counterfactuals I consider three strategies of defense. The strategy that is ultimately accepted as most promising is a revamped approach based on the distinction between possible worlds and possibilities. I counter Kment’s claim that the introduction of fine-grained possibilities within possible worlds is haecceitism in disguise. My conclusion is that anti-haecceitism survives the criticism, and is an overall more attractive position than its competitor.