Exerting control over the near-infrared (NIR) plasmonic response of nanosized metals and semiconductors can facilitate access to unexplored phenomena and applications. Here we combine electrostatic self-assembly and Cd2+/Cu+ cation exchange to obtain an anisotropic core shell nanoparticle cluster (NEC) whose optical properties stem from two dissimilar plasmonic materials: a gold nanorod (AuNR) core and a copper selenide (Cu2-xSe, x >= 0) supraparticle shell. The spectral response of the AuNR@Cu2Se NPCs is governed by the transverse and longitudinal plasmon bands (LPB) of the anisotropic metallic core, since the Cu2Se shell is nonplasmonic. Under aerobic conditions the shell undergoes vacancy doping (x > 0), leading to the plasmon-rich NIR spectrum of the AuNR@ Cu2-xSe NPCs. For low vacancy doping levels the NIR optical properties of the dually plasmonic NPCs are determined by the LPBs of the semiconductor shell (along its major longitudinal axis) and of the metal core. Conversely, for high vacancy doping levels their NIR optical response is dominated by the two most intense plasmon modes from the shell: the transverse (along the shortest transversal axis) and longitudinal (along the major longitudinal axis) modes. The optical properties of the NPCs can be reversibly switched back to a purely metallic plasmonic character upon reversible conversion of AuNR@Cu2Se into AuNR@Cu2Se. Such well-defined nanosized colloidal assemblies feature the unique ability of holding an all-metallic, a metallic/semiconductor, or an all-semiconductor plasmonic response in the NIR. Therefore, they can serve as an ideal platform to evaluate the crosstalk between plasmonic metals and plasmonic semiconductors at the nanoscale. Furthermore, their versatility to display plasmon modes in the first, second, or both NIR windows is particularly advantageous for bioapplications, especially considering their strong absorbing and near-field enhancing properties.