Resumen: In his chapter `Non-transitive identity¿ [8], Graham Priest develops a notion of non-transitive identity based on a second-order version of LP. Though we are sympathetic to Priest¿s general approach to identity we think that the account can be refined in different ways. Here we present two such ways and discuss their appropriateness for a metaphysical reading of indefiniteness in connection to Evans¿ argument.