HySwash has been recently developed as a fast and effective hybrid method to predict nearshore wave processes under unimodal wave conditions. However, global wave climates, and especially those in the tropical regions where coral reefs are hosted, are usually exposed to multiple incoming wave systems, resulting in several energy peaks corresponding to coexisting swells and wind seas. Moreover, although the full distribution of wave runup can have a significant impact on the assessment of vulnerable low-lying tropical regions, predictive models of flooding usually synthesize wave runups to an extreme percentile value, overlooking its full distribution. To enhance the capabilities of HySwash, in the present work, the inclusion of bimodality, as well as the prediction of the complete wave runup distribution is presented. This involves adapting the sampling, selection, and interpolation algorithms together with the hydrodynamic modeling that constitutes the original HySwash methodology. The positive mathematical validation reinforces the applicability of HySwash for a variety of coastal applications. Furthermore, a comparison is conducted between extreme wave runups induced by bimodal sea states and unimodal sea states, providing insights into the impact of multimodality on wave runup extremes.