With the rapid growth of new energy generation capacity, integrating thermal power units and new energy generation units at the same grid connection point as a coupled system can effectively improve the operational reliability and economic efficiency of the new power system. To more accurately reflect the collaborative operational capability of multi-coupled systems when flexibility-modified thermal power units undergo fast load changes, a multi-stage optimal dispatch method for multi-coupled systems is proposed. First, based on the ramping characteristics and field-measured data of thermal units after flexibility retrofits, an analytical expression for coal consumption under fast load changes is derived and validated. On this basis, a three-stage economic optimal dispatch method is proposed with the objective of maximizing the daily integrated generation revenue of the multi-coupled system, while incorporating dynamic cost allocation of peak-shaving benefits across time periods. This approach enables relaxation and simplification of nonlinear objectives and constraints during the solving process. Finally, simulation verifications are conducted on a local multi-coupled system, and the results show that the proposed method can accurately characterize coal consumption variations under fast load changes and achieve dispatch solutions with improved synergy and economic performance.