Frequently, buildings in urban areas are designed by considering their stand-alone response, that is, as single structures with no neighboring buildings. Nevertheless, the existence of a high density of buildings in large metropolitan areas inevitably results in the likelihood of an important seismic interaction between adjacent buildings through the underlying soil. This paper explores the effects of Structure-Soil-Structure Interaction (SSSI) on the seismic response of two yielding structures embedded in a linear elastic soil. A simple two-dimensional nonlinear reduced-order parametric model is proposed, where different building parameters are considered. A nonlinear phenomenological Bouc–Wen model is assumed for the buildings. A database of 15 strong ground motion records and an additional spectrally matched seismic ground motion are considered. An extensive parametric study comprising over two million nonlinear cases is conducted. The results show important differences between nonlinear SSSI and nonlinear SSI for particular parameter configurations. Nevertheless, due to energy dissipation and increases in damping in the nonlinear case, the effects of SSSI are less relevant compared with the linear case.