By the age of 5 years, children will say that even though a certain physical outcome occurred, a different one could have happened. Such claims about possibility are often difficult for scientists and theorists to capture: what does could have happened mean? One important approach to these terms conceives of concepts about possibility as epistemic: to say that the ball could have come down either ramp is to say I didn’t know which side the ball would come down. This analysis is attractive because it renders metaphysically perplexing claims into ordinary statements about the limits of knowledge. But another approach conceives of concepts about possibility as objective: what might have happened based on the universe and its laws, irrespective of my knowing it. Here we presented children with a physical probability device that disentangled responses based on limits of knowledge from responses based on objective possibility. This allowed us to test whether some children maintain a commitment to genuinely objective possibility. 273 preschoolers (range 2 years, 3 months – 6 years, 0 months) made judgments about where a ball could or could not emerge from a device with multiple ramps. Children’s responses revealed that, while some children still had a developing notion of possibility, a large subgroup were Discriminating Modalizers (n = 106, mean age = 4;4), who made judgments of both epistemic and objective possibility appropriately and also showed success with false belief, past knowledge, and non-counterfactual possibility. These children gave answers consistent with the adult pattern (n = 10) and appeared to engage a notion of possibility that goes beyond mere epistemic understanding.