In this paper, we introduce a new framework for modelling the exchange of multiple arguments across agents in a social network. To date, most modelling work concerned with opinion dynamics, testimony, or communication across social networks has involved only the simulated exchange of a single opinion or single claim. By contrast, real-world debate involves the provision of numerous individual arguments relevant to such an opinion. This may include arguments both for and against, and arguments varying in strength. This prompts the need for appropriate aggregation rules for combining diverse evidence as well as rules for communication. Here, we draw on the Bayesian framework to create an agent-based modelling environment that allows the study of belief dynamics across complex domains characterised by Bayesian Networks. Initial case studies illustrate the scope of the framework.