We use an analytical model to propose candidate compositionally complex alloys of the Mo-Nb-Ta-W family with optimal yield stress. We then introduce a computationally tractable method based on first-principles calculations to model phase equilibria in complex alloys at arbitrary concentrations. We utilize this method to predict the phase diagram at the optimized compositions and observe a tendency towards ordering for some of the proposed alloys. By combining yield stress data and thermodynamic equilibria, we suggest two alloy compositions with optimal mechanical properties and a strong solid solution forming ability for further experimental validation.