We consider a scalar conservation law with discontinuous flux function. The fluxes are non-convex, have multiple extrema and arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at the interface. We show that the entropy solutions with respect to each choice of interface connection exist and form a contractive semi-group in L1. Existence is shown by proving convergence of a Godunov type scheme by a suitable modification of the singular mapping approach. This extends the results of  to the general case of non-convex flux geometries.