Adults can represent approximate numbers of items independently of language. This approximate number system can discriminate and compare entities as varied as dots, sounds, or actions. But can multiple different types of entities be enumerated in parallel and stored as independent numerosities? Subjects who were prevented from verbally counting watched an experimenter hide sequences of objects in two locations. The number of object types, which contrasted in category membership, color, shape, and texture, varied from 1 to 5, and object types were completely temporally intermixed. Subjects were then asked how many objects of each type were in each location. In three experiments, subjects successfully enumerated the objects of each type in each location when 1-3 types were presented, but failed with 4 or 5 types, regardless of the total number of objects seen. Thus, adults can perform simultaneous enumeration of multiple sets that unfold in temporally intermixed fashion, but are limited to 3 such sets at a time. Furthermore, they perform these parallel enumerations in the absence of training or instruction, and can do so for sets of objects that are hidden in distinct locations. The convergence of this 3-"set" capacity limit with the 3-"item" capacity limit widely observed in studies of working memory suggests that each enumeration requires a single slot in memory, and that storage in memory is required before enumeration can occur.