Protein-protein interactions play a crucial role in all cellular functions and biological processes and mutations leading to their disruption are enriched in many diseases. While a number of computational methods to assess the effects of variants on protein-protein binding affinity have been proposed, they are in general limited to the analysis of single point mutations and have been shown to perform poorly on independent test sets. Here, we present mmCSM-PPI, a scalable and effective machine learning model for accurately assessing changes in protein-protein binding affinity caused by single and multiple missense mutations. We expanded our well-established graph-based signatures in order to capture physicochemical and geometrical properties of multiple wild-type residue environments and integrated them with substitution scores and dynamics terms from normal mode analysis. mmCSM-PPI was able to achieve a Pearson's correlation of up to 0.75 (RMSE = 1.64 kcal/mol) under 10-fold cross-validation and 0.70 (RMSE = 2.06 kcal/mol) on a non-redundant blind test, outperforming existing methods. Our method is freely available as a user-friendly and easy-to-use web server and API at http://biosig.unimelb.edu.au/mmcsm_ppi.