The rapid development of advanced AI agents and the imminent deployment of many instances of these agents will give rise to multi-agent systems of unprecedented complexity. These systems pose novel and under-explored risks. In this report, we provide a structured taxonomy of these risks by identifying three key failure modes (miscoordination, conflict, and collusion) based on agents' incentives, as well as seven key risk factors (information asymmetries, network effects, selection pressures, destabilising dynamics, commitment problems, emergent agency, and multi-agent security) that can underpin them. We highlight several important instances of each risk, as well as promising directions to help mitigate them. By anchoring our analysis in a range of real-world examples and experimental evidence, we illustrate the distinct challenges posed by multi-agent systems and their implications for the safety, governance, and ethics of advanced AI.