Repeated calls for interdisciplinary research and communication, both within social science and between social, natural and physical scientists, as well as with the rest of the world, frequently meet a fundamental problem: there is no commonly accepted framework or common language within and through which to integrate the largely separate social understandings generated by our social sciences. This paper is an attempt to outline a possible framework, in the hope that it might stimulate debate about why this conception is wrong or how it is incomplete, and so to develop a more generally acceptable common story. The premises of this speculation are: social systems exist – there are understandable processes by which we live, capable of both theoretical and empirical exploration through which to develop better rules and tools for living; these social systems evolve by adaptation, invention and replication to better fit their contexts and circumstances, through the characters and cultures of people, interacting through social transactions. As a consequence, we would expect to observe, following the natural world, identifiable phyla of social transactions and interactions – a taxonomy of social systems. This taxonomy should be capable of retrodiction - plausible explanation of how and why these transactions came to be, and how they correspond to contemporary analysis. This conjecture identifies a plausible taxonomy and an outline evolutionary story of the emergence of the major transactional phyla.