A recursive single source surface integral equation formulation for the problem of electromagnetic wave scattering by multiply-nested bodies yields an equivalent outer surface model that is independent of the material and the illumination in the exterior region, and therefore invariant under rotation and translation. The proposed algorithm is applicable to both far-field and near-field problems, and also gives, through a fast backward recursion, the field values at interior points. Such a reduced model may be duplicated and reused in an assortment of complex scattering problems without repeating the reduction calculation. Thus, the high computational efficiencies realized by the recursive formulation, with respect to the previous, direct, single source surface integral equation formulations, are further enhanced for problems involving some degree of repetition, as in geometry and material optimization of scattering structures under various types of illumination. Numerical examples are included in order to demonstrate the features and the efficiency of the recursive multiply-nested algorithm in comparison to direct, simultaneous solution of all unknowns by the electric field integral equation method.