Advanced antenna systems enable spatial multiplexing through beamforming, allowing the coexistence of multiple, asynchronous, peer-to-peer communications at the medium access control layer, thus introducing multi-packet communication (MPC). The result of each communication is usually established adopting a receiving threshold on the signal-to-interference ratio (SIR). However, more sophisticated reception criteria would be desirable, since the instantaneous SIR of a packet may change because of the asynchrony of the scenario. This paper investigates this partly unexplored issue moving from the exploration of some analytically tractable situations and then performing a comprehensive investigation carried out by a suitable simulation platform. The aim is to realistically estimate the combined effect of the channel access strategy, of the acknowledgement packet, and of the channel code rate, on the throughput, the drop probability, and the packet delay of an MPC network.