Physically-based modelling of rivers has advanced in recent decades by developing separate approaches for representing single-thread and multi-thread channels. This paper reports on a new morphodynamic model developed with the goal of simulating river and floodplain co-evolution within a general framework suitable for investigating diverse fluvial styles. Simulations illustrate the potential for representing meandering, braided and anabranching channels using this model. Moreover, by adopting relatively simple parameterizations of many processes, this work provides insight into what may constitute sufficient (minimal) model complexity, and highlights uncertainties that should be addressed by future research. Copyright © 2013 John Wiley & Sons, Ltd.