While alloying is a powerful handle for materials engineering, it is an ongoing challenge to navigate the large and complex parameter space of these materials. This applies in particular for thermoelectrics and even more so clathrates. Here, we use a combination of density functional theory calculations, alloy cluster expansions, Monte Carlo simulations and Boltzmann transport theory calculations to identify compositions that yield high power factors in the pseudo-ternary clathrates Ba8AlxGayGe16-x-y and Ba8GaxGeySi16-x-y, while accounting for weight and raw material costs. The results show how a cost-efficient performance can be achieved by reducing the number of Al and Ga atoms per unit cell, while compensating the resulting increase in the carrier concentration via an extrinsic dopant. The approach used in this study is transferable and could be a useful tool for mapping the thermodynamic and transport properties of other multinary systems.