Solar absorption refrigeration systems provide one of the economical options for air conditioning. In order to reduce the complexity and economic cost, a more advanced solar single-double-effect switching system is proposed. The innovation of this system is that it replaces the single-effect and high-pressure generators in previously developed single-double-effect switching system with a specific generator. The optimal heat source switching temperature of the new system was determined by the genetic algorithm to be 125.5 °C. Compared with the original single-double-effect switching system, the average coefficient of performance of the system is increased by 8.6%, and the fluctuation of refrigeration capacity during the switching period is reduced by 48%. The new solar single-double-effect switching system is investigated based on thermodynamic characteristics, energy, exergy, and economy aspects. The results showed that heat exchangers of the system have strong coupling. The cooling water temperature has a greater impact on the performance of the dual-effect mode. In the single-effect mode, the special-pressure generator has the largest exergy destruction (39%), while in the double-effect mode, the absorber has the largest exergy destruction (41%). Besides, the economic analysis demonstrated that the new system is economically viable with a payback period of 9.33 years.