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Non-additive mixing plays a key role in the properties of molecular fluids and solids. In this work, the potential for athermal order–disorder phase transitions is explored in non-additive binary colloidal nanoparticles that form substitutionally ordered compounds, namely, for equimolar mixtures of octahedra + spheres, which form a CsCl lattice compound, and cubes + spheres, which form a NaCl crystal. Monte Carlo simulations that target phase coexistence conditions were used to examine the effect on compound formation of varying degrees of negative non-additivity created by component size asymmetry and by size-tunable indentations in the polyhedra’s facets, intended to allow the nestling of neighboring spheres. Our results indicate that the stabilization of the compound crystal requires a relatively large degree of negative non-additivity, which depends on particle geometry and the packing of the relevant phases. It is found that negative non-additivity can be achieved in mixtures of large spheres and small cubes having no indentations and lead to the athermal crystallization of the NaCl lattice. For similarly sized components, athermal congruent transitions are attainable and non-additivity can be generated through indentations, especially for the cubes + spheres system. Increasing indentation leads to lower phase coexistence free energy and pressure in the cubes + spheres system but has the opposite effect in the octahedra + spheres system. These results indicate a stronger stabilizing effect on the athermal compound phase by the cubes’ indentations, where a deeper nestling of the spheres leads to a denser compound phase and a larger reduction in the associated pressure-volume free-energy term.