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More than a billion people around the world experience intermittence in their water supply, where water is delivered for only a few hours per day or a few days per week. This prompts water users to adapt by installing storage tanks or accessing alternative water services to balance service deficits. Adaptation and its resulting costs and impacts are unequally distributed across urban households and have shown to be largely unaccounted for by local water managers. Most studies on household adaptation to intermittent water supply (IWS), which are typically conducted through survey or interview methods, assume income-based heterogeneity to determine adaptive behaviours and do not account for the multiple factors that influence household adaptation. However, our recent research has demonstrated the multiple factors that shape various household responses to IWS in Amman, Jordan, using hierarchical clustering analysis (HCA). Different clusters of households are distinguished by a set of characteristics, including income, water social network, supply duration, relocation, and water quality problems, and related group-specific adaptive strategies such as contacting the water utility or relying on private water services. Building on this work, we develop a computational model that reproduces piped water use and deficits over time across representative agents from each cluster. We test the model across scenarios of increasing intermittence and population growth, while reproducing trajectories across parameters of pressure and total water availability, giving insights into the inequality and parameters of the system, creating different regimes of water deficit caused by the municipal water supply regime across clusters. We then add the adaptive behaviours of households as recorded in the empirical survey data, to show how adaptation changes water supply resilience across heterogeneous households. This forms a crucial step towards an equitable and resilience-oriented water management as it reduces several epistemic uncertainties within the system by strengthening the feedback between household adaptation efforts and local water management.