Plasmonic properties, such as refractive index sensitivity (RIS), surface enhancement of the Raman signal (SERS), fluorescence quenching, and photocatalytic activity, of monolayers of weakly interacting monodisperse silver nanocubes were qualitatively modified in a very well controlled manner by supporting them on thin silicon films with varying thickness. Such fine tunability is made possible by the strong dependence of the nanocube dipolar (D) and quadrupolar (Q) plasmon mode hybridization on the refractive index of the supporting substrate. By increasing the Si film thickness from zero to ~25 nm we were able to "shift" the D resonance mode by up to 200 nm for ~80 nm cubes without significantly affecting the Q mode. The silicon supported nanocubes showed a significant improvement in RIS via the Q mode with a figure of merit greater than 6.5 and about an order of magnitude enhancement of the SERS signal due to the stronger electric field created by the D mode. Such substrates also showed a ~10 times decrease in rhodamine 6G fluorescence as well as the rates of amorphous carbon formation. The study proposes a new way to design and engineer plasmonic nanostructures.