The multi-trace domain-decomposition surface integral equation (MT-DD-SIE) originally developed for analyzing electromagnetic scattering from dielectric composite objects is extended to efficiently account for perfect electrically conducting (PEC) bodies within composite objects. This is achieved by adopting Robin transmission conditions (RTCs) to PEC surfaces. These PEC-RTCs, which are the only governing equations for a PEC body, are used to ‘`couple’' it to the dielectric bodies. Upon discretization, the PEC-RTCs produce a well-conditioned matrix block and therefore does not negatively affect the convergence of the iterative solution of the MT-DD-SIE matrix equation. The resulting method is significantly faster and has a smaller memory imprint than the traditional globally-coupled contact-region-modeling method that makes use of the coupled electric field and Poggio-Miller-Chang-Harrington-Wu-Tsai SIEs in analyzing electromagnetic scattering from composite PEC/dielectric objects. This is demonstrated by numerical examples involving electrically large scatterers.