Rheological characteristics of a concentrated suspension can be tuned using anisotropic particles having various shapes and sizes. Here, the role of anisotropic nanoparticles, such as surface-functionalized multiwall carbon nanotubes (MWNTs) and graphene oxide nanoplatelets (GONPs), on the rheological behavior of fumed silica suspensions in poly(ethylene glycol) (PEG) is investigated. In these mixed-particle suspensions, the concentrations of MWNTs and GONPs are much lower than the fumed silica concentration. The suspensions are stable, and hydrogen-bonded PEG solvation layers around the particles inhibit their flocculation. Fumed silica suspensions over the concentration range considered here display shear-thickening behavior. However, for a larger concentration of MWNTs and with increasing aspect ratios, the shear-thickening behavior diminishes. In contrast, a distinct shear-thickening response has been observed for the GONP-containing suspensions for similar mass fractions (MFs) of MWNTs. For these suspensions, shear thickening is achieved at a lower solid MFs compared to the suspensions consisting of only fumed silica. A significant weight reduction of shear-thickening fluids that can be achieved by this approach is beneficial for many applications. Our results provide guiding principles for controlling the rheological behavior of mixed-particle systems relevant in many fields.