We build an effective field theory of multi-field inflationary fluctuations based on the adiabatic perturbation and on any number of matter fluctuations in the non-adiabatic sector, without imposing extra symmetries on the latter. Focusing on terms with at most two derivatives in fields' fluctuations, we argue that taking the decoupling limit -- in which gravitational interactions are neglected -- is justified in a quasi de Sitter spacetime with slow-varying Hubble scale. With these working hypotheses, we find simple forms of multi-field mixings (quadratic order) and interactions (cubic order). We explain how to break degeneracies amongst various terms, and we compare the predictions of the effective field theory to those of non-linear sigma models of inflation and more general multi-field Lagrangian in the traditional model approach. We stress that several multi-field cubic interactions are dictated by non-linearly realised spacetime symmetries and are therefore given in terms of parameters already present in the quadratic action. We propose various directions to systematically explore the phenomenology generic to multi-field inflation and beyond the lamppost of known models.