In this paper, I focus on a recent debate in extended cognition known as “cognitive assembly” and how cognitive assembly shares a certain kinship with the special composition question advanced in analytical metaphysics. Both the debate about cognitive assembly and the special composition question ask about the circumstances under which entities (broadly construed) compose or assemble another entity. The paper argues for two points. The first point is that insofar as the metaphysics of composition presupposes that composition is a synchronic relation of dependence, then that presupposition is inconsistent with the temporal dynamics inherent in the process of cognitive assembly. The second point is that by developing a diachronic or temporally dynamic ontology for understanding the phenomenon of cognitive assembly, this lends support for a third wave of extended cognition.