In this study, we link a water resource management simulator to multi-objective search to reveal the key trade-offs inherent in planning a real-world water resource system. We consider new supplies and demand management (conservation) options while seeking to elucidate the trade-offs between the best portfolios of schemes to satisfy projected water demands. Alternative system designs are evaluated using performance measures that minimize capital and operating costs and energy use while maximizing resilience, engineering and environmental metrics, subject to supply reliability constraints. Our analysis shows many-objective evolutionary optimization coupled with state-of-the art visual analytics can help planners discover more diverse water supply system designs and better understand their inherent trade-offs. The approach is used to explore future water supply options for the Thames water resource system (including London's water supply). New supply options include a new reservoir, water transfers, artificial recharge, wastewater reuse and brackish groundwater desalination. Demand management options include leakage reduction, compulsory metering and seasonal tariffs. The Thames system's Pareto approximate portfolios cluster into distinct groups of water supply options; for example implementing a pipe refurbishment program leads to higher capital costs but greater reliability. This study highlights that traditional least-cost reliability constrained design of water supply systems masks asset combinations whose benefits only become apparent when more planning objectives are considered.