Flexibility is a crucial capability that distributed energy systems need to possess. Flexible distributed energy systems can attain the objectives of daily economic operation for users, temporary demand response for the power grid, and low-carbon operation for environmental benefits. Among these objectives, economy and low-carbon objectives are long-term objectives that need to be met routinely, while grid-friendly interactions only occur temporarily but need to be met as a priority. Current multi-objective optimization planning models disregard the inherent differences in temporal property of these objectives, which may weaken the system's flexibility. Here, a novel multi-objective optimization model is proposed to enhance the flexibility of distributed energy systems. First, a new flexibility index is formulated, in which diverse objectives are evaluated synergistically across different scenarios. Second, a flexible mixed-integer multi-objective programming model is developed, which returns the most flexible system design and its operation strategies for each objective. The application in a real case in Tianjin, China revealed that, compared with the conventional multi-objective planning method, the proposed method could improve the system flexibility by 6%–10 %. The universality of the proposed method was further verified by traversal analysis.