Synthetic biology aspires toward the biologically possible by reimagining and building novel biological parts, devices, and organisms by combining well-characterized biological components. Given its combinatorial nature, we examine synthetic biology's modeling practice using David Armstrong's combinatorial theory of possibility. It approaches possibilities in terms of combining the actual elements of the world. We argue that apart from combination, two other features of Armstrong's theory are crucial for synthetic biology: structural universals and the requirement of their instantiation. The search for general (...) design principles, which we refer to as structural universals, is one of the primary goals of understanding biological organization, natural or otherwise. -/- . (shrink)