A generic method to estimate the relative feasibility of formation of high entropy compounds in a single phase, directly from first principles, is developed. As a first step, the relative formation abilities of 56 multi-component, AO, oxides were evaluated. These were constructed from 5 cation combinations chosen from A={Ca, Co, Cu, Fe, Mg, Mn, Ni, Zn}. Candidates for multi-component oxides are predicted from descriptors related to the enthalpy and configurational entropy obtained from the mixing enthalpies of two component oxides. The utility of this approach is evaluated by comparing the predicted combinations with the experimentally realized entropy stabilized oxide, (MgCoCuNiZn)O. In the second step, Monte Carlo simulations are utilized to investigate the phase composition and local ionic segregation as a function of temperature. This approach allows for the evaluation of potential secondary phases, thereby making realistic predictions of novel multi-component compounds that can be synthesized.