We consider the network information theoretic problem of finding the rate distortion bound for separate coding of multiple correlated sources. First, we find the outer region for separate coding with distortion when only one of the sources is to be reproduced and the other sources are used as helpers. We then find the outer region for separate coding when all the sources are to be reproduced with specified distortions. The rate distortion bounds have previously been calculated for two correlated sources. We find an inductive approach to consider several sources one after the other to derive the general result. We also show the practical implications of our work for several implementations. Our results can be directly utilized by designers to choose not only how many of the available sources should actually be coded but also which sources have the highest potential to reduce the distortion.