This article focuses on suspensions of coarse particles within a clay dispersion. The behavior of such suspensions is generally dictated by the colloidal fine fraction, notably its yield stress. The dependence of this yield stress on the solid concentration (in coarse particles) is examined. It has been experimentally shown that adding coarse particles usually induced an increasingly marked enhancement of yield stress. However, in some cases, adding a small amount of coarse particles led to a decrease in bulk yield stress. We propose two mechanisms responsible for variations in bulk yield stress. First, at low concentrations, depletion of clay particles may be sufficient to induce an increase in the bulk yield stress. Two values for the depletion layer thickness have been found depending on the coarse particle type. At large concentrations, the substantial increase in bulk yield stress has been ascribed to the development of a coarse particle network within the dispersion. In this case, yielding results from the breakdown of indirect (lubricated) contacts between particles.