Hard spheres mixed with penetrable hard spheres display an isostructural solid-solid transition. This phase transition is fully driven by the entropy gain of the depletants without invoking explicit pair potentials between the colloidal particles. The solid-solid phase coexistence terminates at a critical endpoint with a size ratio q approximate to 0.09. Colloid-polymer mixtures are an excellent candidate for the experimental realization of this intricate solid-solid transition, first predicted by Bolhuis and Frenkel for hard spheres with short range pair attractions