In this paper, we develop an agent-based multi-layered interbank network model based on a sample of large EU banks. The model allows for taking a more holistic approach to interbank contagion than is standard in the literature. A key finding of the paper is that there are non-negligible non-linearities in the propagation of shocks to individual banks when taking into account that banks are related to each other in various market segments. In a nutshell, the contagion effects when considering the shock propagation simultaneously across multiple layers of interbank networks can be substantially larger than the sum of the contagion-induced losses when considering the network layers individually. In addition, a bank “systemic importance” measure based on the multi-layered network model is developed and is shown to outperform standard network centrality indicators.