Chapter 4 fundamentally rethinks the identity of “composite” or “hybrid” creatures as they were embodied and experienced in Crete and the southern Cyclades from the late third to mid-second millennium BCE. I argue that, when pondered closely and in their contexts, many of the creatures to which we apply this label in fact would have been experienced not as counterintuitive compounds of body parts stemming from other species, but, instead, as whole beings that were perceived as being similar to a range of other creatures. These lines of similitude could concern matters of form as well as other aspects of the creatures’ natures (e.g., color, efficacies). With this, the traditional category of the “composite” being is set aside as a larger swath of interconnected creatures comes into view. These remarkable creatures share amongst them the quality of having apparent connections both beyond the Aegean, with thingly embodiments of beasts from overseas, and more locally, with other Aegean fabricated and biological animals. An iconic creature of the Aegean Bronze Age, the griffin, provides a jumping off point for different parts of this discussion, as we reconsider the creativity realized in such beasts.