Rheology and adsorption studies are performed on a model multicomponent system of hydrophobically modified cellulose (hmHEC), anionic surfactant (SDS), and negatively charged silica. Optical reflectometry measurements on silica quantify the total adsorbed mass from polymer-surfactant mixtures and indicate that the adsorption is irreversible. Linear and nonlinear rheological measurements show that the addition of colloidal silica to polymer-surfactant mixtures leads to complex and unexpected changes in behavior that cannot be explained simply as depletion of the bulk solution via adsorption to the colloidal surface. Instead, the combination of rheology and adsorption measurements indicates that the colloidal silica becomes an integral part of the transient network shifting the dynamics of the system.