Intelligent district energy management with sector-coupling gains importance with the decentralization of the energy supply, as we urge towards a fast reduction of greenhouse gas emissions and aim at more efficient energy usage. By jointly optimizing and coordinating the electricity, mobility, and heating domain, the share of local renewable energy share can be increased, and costs can be decreased across sectors. This work mathematically describes a joint Sector-Coupled District Energy Management (SeCo-DEM) as a multi-objective mixed-integer linear program. The model includes combined heat and power, immersion heaters, battery storage, hot water storage, peak-load supply, and bi-directional electric vehicle chargers. Based on data from two research projects, we analyze the individual influence of different flexibility options in terms of costs and self-consumption. We find that combining bi-directional charging and immersion heaters is a cost-effective combination that can increase self-consumption from 68.14% to 93.70%.