A modern method of random access for packet networks, named ``Irregular Repetition Slotted Aloha (IRSA)'', had been proposed: it is based repeating transmitted packets, and on the use of successive interference cancellation at the receiver. In classical idealized settings of slotted random access protocols (where slotted ALOHA achieves 1/e), it has been shown that IRSA could asymptotically achieve the maximal throughput of 1 packet per slot. Additionally, IRSA had previously been studied for many different variants and settings, including the case where the receiver is equipped with ``multiple-packet reception'' (MPR) capability. In this article, we extensively revisit the case of IRSA with MPR. First, one of our major results is the proof that K-IRSA cannot reach the natural bound of throughput, and we prove a new, lower bound for its performance. Second, we give a simple expression for its excellent loss rate at lower loads. Third, we show how to formulate the search for the appropriate parameters of IRSA as an optimization problem, and how to solve it efficiently. By doing that for a comprehensive set of parameters, and by providing this work with simulations, we give numerical results that shed light on the performance of IRSA with MPR.