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We present an extension of the linear embedding via Green's operators (LEGO) procedure for efficiently dealing with 3-D electromagnetic composite structures. In LEGO's notion, we enclose the objects forming a structure within arbitrarily shaped domains (bricks), which (by invoking the equivalence principle) we characterize through scattering operators. In the 2-D instance, we then combined the bricks numerically, in a cascade of successive embedding steps, to build increasingly larger domains and obtain the scattering operator of the whole aggregate of objects. In the 3-D case, however, this process becomes quite soon impracticable, in that the resulting scattering matrices are too big to be stored and handled on most computers. To circumvent this hurdle, we propose a novel formulation of the electromagnetic problem based on an integral equation involving the total inverse scattering operator of the structure, which can be written analytically in terms of scattering operators of the bricks and transfer operators among them. We then solve this equation by the method of moments combined with the eigencurrent expansion method, which allows for a considerable reduction in size of the system matrix and thereby enables us to study very large structures.