Phase stability in multi-components alloy systems is still largely unknown, especially at the internal interfaces. Grain boundary (co-)segregation is one of the main causes of instability and therefore safety issues in microstructures. In this work, the segregation in FCC Fe-Ni-Cr alloy system, which is the base for several steels, super-alloys and high entropy alloys, is studied. The density-based phase-field model is advanced to compute the segregation of Fe, Ni and Cr at the grain boundary corresponding to the bulk composition. Here the relative density of the grain boundary to the bulk is the mean-field parameter of the model. The necessary thermodynamic parameters of the bulk are obtained from the CALPHAD database. We performed high-throughput screening of the elemental segregation at the grain boundary across the stable bulk compositions at different temperatures (723 K, 1023 K and 1323 K). The results reveal complex enrichment/depletion of each element depending on the alloy composition and temperature. Opposite segregation of Ni and Cr and co-segregation of Ni and Fe is observed for almost all compositions at 723 K, but a changing trend is observed with increasing temperature. We discuss the origin and consequences of these segregation behaviours in the light of magnetic ordering effects.