Pulse shape discrimination (PSD) is at the core of radioactive particles monitoring. Conventional PSD methods are geared towards low event rates, and struggle in the presence of pileups resulting from high rate. In this work we develop a PSD algorithm that combines classic approaches with deep learning techniques, that is highly suitable for coping with the dramatic challenges associated with classifying pulses in high event rates. Common PSD algorithms for high event rates limit their research to two piled-up pulses. Our algorithm is designed and tested under severe pileup conditions, where three or more pulses were piled-up. We tested the algorithm on simulated data based on Cs2LiYCl6:Ce (CLYC) based detector pulse shapes and compare its performance to both traditional PSD algorithms and data-driven deep neural network (DNN) based algorithms. In high event rates, ranging up to 10 Mcps, the algorithm demonstrates up to 8 times fewer miss-classifications than the traditional normalized cross-correlation (NCC) approach, and up to 1.7 times fewer miss-classifications than a purely data-driven DNN-aided method.