Self-Aligned Via (SAV) process is commonly used in back end of line (BEOL) patterning. As the technology node advances, tightening CD and overlay specs require continuous improvement in model accuracy of the SAV process. Traditional single layer Variable Etch Bias (VEB) model is capable of describing the micro-loading and aperture effects associated with the reactive ion etch (RIE), but it does not include effects from under layers. For the SAV etch, a multi-layer VEB model is needed to account for the etch restriction from metal trenches. In this study, we characterize via post-etch dimensions through pitch and through metal trench widths, and show that VEB model prediction accuracy for SAV CDs after SAV formation can be significantly improved by applying a multi-layer scheme. Using a multi-layer VEB, it is demonstrated that the output via size changes with varying trench dimensions, which matches the silicon results. The model also reports via shape post-etch as a function of trench environment, where elliptical vias are correctly produced. The multi-layer VEB model can be applied both multi-layer correction and verification in full chip flow. This paper will also suggest that the multi-layer VEB model can be used in other FEOL layers with interlayer etch process effects, such as gate cut, to support the robustness of new model.