Capillary suspensions are ternary systems including a solid and two liquid phases representing a novel formulation platform for pastes with unique processing and end-use properties. Here we have investigated aqueous suspensions of non-Brownian graphite particles including different polymers commonly used as thickening agents or binders in paste formulations. We have studied the interaction between these additives and organic solvents in order to elucidate its effect on the characteristic formation of a particle network structure in corresponding ternary capillary suspension systems. Organic solvents with different polarity have been employed, and in the presence of nonadsorbing poly(ethylene oxide), all of them, whether they preferentially wet the graphite surface or not, induce the formation of a network structure within the suspension as indicated by a strong change in rheological properties. However, when the adsorbing polymers carboxymethylcellulose and poly(vinylpyrrolidone) are included, the drastic change in rheological behavior occurs only when polar organic solvents are used as secondary liquids. Obviously, these solvents can form pendular bridges, finally resulting in a sample-spanning particle network. Vibrational sum frequency spectroscopy provides evidence that these polar liquids remove the adsorbed polymer from the graphite particles. In contrast, nonpolar and nonwetting solvents do not force polymer desorption. In these cases, the formation of a percolating network structure within the suspensions is presumably prevented by the strong steric repulsion among graphite particles, not allowing for the formation of particle clusters encapsulating the secondary liquid. Accordingly, polymeric additives and secondary fluids have to be carefully selected in capillary suspension formulations, then offering a new pathway to customize paste formulations. The polymer may serve to adjust an appropriate viscosity level, and the capillary bridging induces the desired degree of shear thinning. Alternatively, the polymer may be selected with respect to its binding properties in the final dry product, and capillary bridging may be used to control the flow and processing behavior of the wet paste.