In this work we classified the necessary and the sufficient conditions that an index of a superconformal theory in 3 to 6 dimensions must obey for the theory to have enhanced supersymmetry. These conditions may be used as a tool to identify theories where SUSY is enhanced, either by turning on an exactly marginal deformation, or by an RG flow triggered by a massive deformation. The classification is obtained by noting that the index distinguishes a superconformal multiplet contribution to the index only up to a certain equivalence class it lies in. We then use our results to study some of the d = 4 theories described by Agarwal, Maruyoshi and Song, and find that the theories in question have only N = 1 SUSY despite having rational central charges.