The rheology of suspensions (solid particles dispersed in a fluid) is controlled primarily through the volume fraction of solids. We show that the addition of small amounts of a secondary fluid, immiscible with the continuous phase of the suspension, causes agglomeration due to capillary forces and creates particle networks, dramatically altering the bulk rheological behavior from predominantly viscous or weakly elastic to highly elastic or gel-like. This universal phenomenon is observed for a rich variety of particle/liquid systems, independent of whether the second liquid wets the particles better or worse than the primary liquid. These admixtures form stable suspensions where settling would otherwise occur and may serve as a precursor for microporous polymer foams, or lightweight ceramics.