The shear flow of non-Brownian glass spheres suspended in a concentrated colloidal dispersion that exhibits non-Newtonian rheology is investigated. At low volume fractions, the addition of non-Brownian spherical particles to the colloidal dispersion leads to an increase. in the steady shear viscosity as well as the dynamic moduli. The flow curves of these suspensions are qualitatively similar to the suspending colloidal dispersion medium, and as such, in this semidilute regime, the suspension data can be shifted on to that of the colloidal dispersion medium at constant shear stress with shift factors comparable to those predicted for spherical particles in a Newtonian fluid. At higher volume fractions of non-Brownian spheres, the shear thickening power law exponent increases with the addition of non-Brownian particles. This increase in the shear thickening power law exponent is shown to be consistent with the effects of confinement on the shear thickening colloidal dispersion by the larger non-Brownian particles. (C) 2016 The Society of Rheology.