The last three decades have witnessed a trend in solar thermal electricity generation of increasing the concentration of sunlight, the operating temperature, and subsequently the efficiency of conversion from sunlight to electricity. The current state of the art concept is a solar-driven combined cycle, with sunlight concentration ratio of a few thousands, temperatures of about 1000-1300°C, and overall annual average conversion efficiency of about 20%. A possible next step in this trend is presented: a solar triple cycle, with a high-temperature MHD generator and two additional cycles in series. This triple cycle is powered by solar heat at temperatures around 2000°C and solar concentration of about 10,000. The overall peak conversion efficiency of the solar triple cycle is shown to be significantly higher than the solar combined cycle scheme. The sensitivity of this result to several system parameters and the technological feasibility of the solar triple cycle are also discussed.