Previous studies have demonstrated the possibility of maintaining a reliable electric power system with high shares of renewables, but only assuming the deployment of specific technologies in precise ratios, careful demand-side management, or grid-scale storage technologies. Any scalable renewable technology that could provide either baseload or dispatchable power would allow greater flexibility in planning a balanced system, and therefore would be especially valuable. Many analysts have suggested that concentrating solar power (CSP) could do just that. Here we systematically test this proposition for the first time. We simulate the operation of CSP plant networks incorporating thermal storage in four world regions where CSP is already being deployed, and optimize their siting, operation and sizing to satisfy a set of realistic demand scenarios. In all four regions, we show that with an optimally designed and operated system, it is possible to guarantee up to half of peak capacity before CSP plant costs substantially increase.