Small-scale distributed energy systems with combined cooling, heating, and power (DES-CCHP) production have attracted international interest. However, fluctuating loads and renewable energies continuously disturb the real-time operation of DES-CCHP and even the connected grid, hindering the broad application of grid-connected DES-CCHP. In this paper, a novel model predictive control (MPC) based two-stage strategy is developed for DES-CCHP, with multiple timescales consideration. In the first stage, a multi-objective MPC is built with inheritance and fusion mechanisms of multi-step scheduling instructions, simultaneously minimizing operation costs and power fluctuations. The second stage performs intelligent decision-making on the results of the first stage, which allows appropriate state-switching instructions to ensure economy. Meanwhile, the decision-making rejects the unnecessary one and triggers a second-round flexibility-based interventional optimization to revise scheduling planning. The case studies show that compared to dispatch without MPC, the economic single-objective MPC, single-stage multi-objective MPC (only applies the first-stage models), and two-stage multi-objective MPC save costs by 5.31 %, 4.80 %, and 4.57 %, respectively. As for fluctuations mitigation, the single-stage and two-stage models significantly smooth power fluctuations by 51.66 % and 69.93 %, respectively. The proposed strategy operates DES-CCHP economically, stably, and grid-friendly under a rugged operating environment.