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Linear embedding via Green's operators (LEGO) is a computational method in which the multiple scattering between adjacent objects — forming a large composite structure — is determined through the interaction of simple-shaped building domains, whose electromagnetic (EM) behavior is accounted for by means of scattering operators. This method has been successfully demonstrated for 2-D electromagnetic band-gaps (EBG) and other structures [1], and for very simple 3-D configurations [2]. In this communication we briefly report on the full extension of LEGO to large complex 3-D structures, which may be EBG-based but may also include finite antenna arrays as well as frequency selective surfaces, to name but a few applications. In particular, we shall outline two modifications that were crucial for scaling up the LEGO method, namely, the introduction of a total inverse scattering operator S−1 and the eigencurrent expansion method (EEM) [3].