We examine the rheological transition from an arrested to a fluid state for different mixtures of star polymers with varying functionality and size ratios. As a general trend, we find that addition of smaller star polymers in an arrested, concentrated solution of larger ones brings about melting of the large star glass. At the same time, the dependence of the amount of additives needed to melt the glass has a nontrivial dependence on the size ratio. Theoretical analysis, based on effective interactions and Mode Coupling Theory, reproduces the experimental results and helps identify two distinct types of glasses in the composite system.