A Magnetic Cluster Expansion (MCE) model for ternary face-centered cubic Fe-Ni-Cr alloys has been developed using DFT data spanning binary and ternary alloy configurations. Using this MCE model Hamiltonian, we perform Monte Carlo simulations and explore magnetic structures of alloys over the entire range of alloy compositions, considering both random and ordered alloy structures. In random alloys, the removal of magnetic collinearity constraint reduces the total magnetic moment but does not affect the predicted range of compositions where the alloys adopt low temperature ferromagnetic configurations. During alloying of ordered fcc Fe-Ni compounds with Cr, chromium atoms tend to replace nickel rather than iron atoms. Replacement of Ni by Cr in alloys with high iron content increases the Curie temperature of the alloys. This can be explained by strong antiferromagnetic Fe-Cr coupling, similar to that found in bcc Fe-Cr solutions, where the Curie temperature increase, predicted by simulations as a function of Cr concentration, is confirmed by experimental observations. Recently, we have developed an ab initio parameterized Heisenberg-Landau lattice Hamiltonian-based Magnetic Cluster Expansion (MCE) model for binary fcc Fe-Ni [3]. To describe the high-and low-spin magnetic configurations of fcc Fe, terms up to the 8 th order in atomic magnetic moment were included in the Landau expansion for the on-site terms in the Hamiltonian. Thermodynamic and magnetic properties of the alloys were explored, using configurational and magnetic Monte Carlo simulations, over a broad temperature range extending well over 1000 K. The predicted fcc-bcc coexistence curve, the phase stability of ordered Fe 3 Ni, FeNi, and FeNi 3 intermetallic compounds, and the predicted temperatures of magnetic transitions simulated as functions of alloy compositions were found to agree well with experimental observations. In particular, simulations show that magnetic interactions stabilize fcc phases of binary Fe-Ni alloys. Parameters of the MCE model for Fe-Ni alloys were derived from DFT calculations performed for a large number of representative atomic configurations, as well as from DFT data on pure fcc Ni and Fe. The success of that model, together with the availability of DFT data accumulated in the context of a recent comprehensive ab initio investigation of Fe-Ni-Cr alloys [4], makes it possible to extend MCE to ternary fcc Fe-Ni-Cr alloys. The MCE model for ternary Fe-Ni-Cr alloys is the first example of application of Magnetic Cluster Expansion to a magnetic alloy containing more than two components. The initial parameterization of the Fe-Ni-Cr MCE Hamiltonian, and initial simulations performed using this Hamiltonian, are described in Ref. [4]. Here we describe an improved more accurate MCE model based on a larger DFT database of structures and magnetic configurations. Monte Carlo simulations using the MCE Hamiltonian span both random and ordered alloy structures. The advantages of MCE include the possibility of simulating a broad range of all...