We present an approach alternative to the hybridization model for the treatment of the coupled interfacial plasmon modes in spheroidal metallic nanoshells. Rather than formulating the problem from the Lagrangian dynamics of the free electronic fluid, we adopt an effective medium approach together with the uniqueness of the solutions to electromagnetic boundary value problem, from which the polarizability of the shells can then be systematically and efficiently derived; and the resonance frequencies for the coupled modes can be obtained from the poles in the polarizability. This approach can treat confocal nanoshells with different geometries for the spheroidal cavity and external surface and allow for a natural extension to incorporate corrections from the finiteness of the optical wavelength which are important for nanoparticles of larger sizes. This thus surpasses the hybridization model which is limited to incorporate only the electrostatic Coulomb interaction between the uncoupled plasmons. Numerical results will be provided for different nanoshell systems, and for the illustration of the various geometric and dynamic effects from our model.