Normal mode oscillations in Saturn excite density and bending waves in the C Ring, providing a valuable window into the planet’s interior. Saturn's fundamental modes (f-modes) excite the majority of the observed waves, while gravito-inertial modes (rotationally modified g-modes) associated with stable stratification in the deep interior provide a compelling explanation for additional density waves with low azimuthal wavenumbers m. However, multiplets of density waves with nearly degenerate frequencies, including an m=3 triplet, still lack a definitive explanation. We investigate the effects of rapid and differential rotation on Saturn’s oscillations, calculating normal modes for independently constrained interior models. Our calculations demonstrate that sectoral f-mode frequencies are measurably sensitive to realistic profiles for differential rotation in Saturn’s convective envelope. We also find that differential rotation can enhance mode interactions, producing detectable oscillations with frequencies separated by less than 1%. Our results suggest that a three-mode interaction involving an f-mode and two g-modes can feasibly explain the finely split m=3 triplet, although arranging such an interaction requires fine-tuning. Lastly, we find that even a small equatorial antisymmetry in Saturn’s differential rotation profile can couple modes with even and odd equatorial parity, producing oscillations that could in principle excite both density and bending waves simultaneously.