We study mixtures of star polymers and linear chains in good solvent conditions. We consider the effect of the addition of small chains on the equilibrium structure as well as on the phase behavior of low- and intermediate-functionality star solutions. By using a recently introduced effective cross interaction between stars and chains [C. Mayer and C. N. Likos, Macromolecules 40, 1196 (2007)], we solve the two-component Ornstein-Zernike equation, finding evidence for cluster formation, which is accompanied by a spinodal instability at moderate chain concentrations. The binodal lines are numerically calculated and the dependence of the observed phenomena on functionality, size, and concentrations is rationalized by considering the attractive contribution, which is displayed by the effective, chain-modified star-star interaction potential.