Volume discretization methods face multiple challenges when applied to exterior scattering analyses, including high computational cost and the need for artificial domain truncation. Methods based on boundary integral equations reduce the spatial dimensionality of the problem; however, they introduce new difficulties, such as the treatment of singular integral kernels and the resulting dense and potentially ill-conditioned system matrices. These challenges become more pronounced in multiple-scattering problems, where waves repeatedly propagate between several obstacles. These limitations often restrict their applicability to low- and mid-frequency regimes. Similar to boundary integral methods, On-Surface Radiation Conditions (OSRC) require only boundary discretization and yield integral equations with smooth kernels. Previous work (the ITOSRC method ) demonstrated that by capturing multiple scattering through an iterative scheme, OSRC can be used to perform both single- and multiple-scattering analyses with high reliability and drastically reduced computational cost compared to standard boundary element methods, by avoiding complex, nonlocal integral formulations. In this study, we extend the ITOSRC framework to solve acoustic transmission problems, achieving significantly reduced computational cost and runtime. We assess the method’s performance and discuss its potential applications.