A cornstarch suspension is the quintessential particulate system that exhibits shear thickening. By adding large non-Brownian spheres to a cornstarch suspension, we show that shear thickening can be significantly enhanced. More precisely, the shear-thickening transition is found to be increasingly shifted to lower critical shear rates. This influence of the large particles on the discontinuous shear-thickening transition is shown to be more dramatic than that on the viscosity or the yield stress of the suspension.