We present tunable coupling between surface plasmon resonances supported by a metal-nanoparticle-coated tip and three-dimensionally (3D) confined optical modes supported by a microtube cavity. The competition and transition between two types of coupling mechanisms, i.e., dielectric-dielectric and plasmon-dielectric coupling, are observed in the tunable system. Owing to the competition between the two coupling mechanisms, the resonant modes can be dynamically tuned to first shift from higher to lower energies and then revert to higher energy. Moreover, the unique spatial field distribution of 3D confined modes allows selective coupling of odd and even order axial modes with surface plasmon resonances.