  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.
