Control of the polarization distribution of light allows tailoring the electromagnetic response of plasmonic particles. By rigorously extending the generalized multiparticle Mie theory, we show that focused cylindrical vector beams (CVB) can be used to efficiently excite dark plasmon modes in nanoparticle clusters. In addition to the small radiative damping and large field enhancement associated to dark modes, excitation with CVB can give place to unusual phenomenology like the formation of electromagnetic cold spots and the generation of Fano resonances in highly symmetric clusters. Overall, the results show the potential of CVB to tailor the plasmonic response of nanoparticle clusters in a unique way.