In this paper, some generalizations of electromagnetic scattering problems by elementary shapes are presented. In particular, the aim of the paper is to provide solutions to the scattering problem by multiple objects with simple shapes, either in concentric configuration or arbitrarily distributed in the space. The vector harmonics, representing the fields, and their properties are applied in order to solve five different problems: the electromagnetic scattering by an infinitely long circular stratified cylinder, by a multilayered sphere, by an ensemble of parallel cylinders, by an ensemble of multi-spheres, and ultimately by a sphere embedded in a circular cylinder. Numerical results in particularly important configurations are shown.