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The rapid electrification of residential heating and mobility sectors is expected to drive the existing distribution grid assets beyond their planned operating conditions This change will also reveal new potentials through sector coupling, flexibilities, and the local exchange of decentralized generation. This paper thus presents an optimization framework for multi-modal energy systems at the low voltage (LV) distribution grid level. In this, we focus on the reinforcement requirements of the grid and the techno-economic assessment of flexibility components and coordination between agents. By employing a multi-level approach, computational complexity is reduced, and various levels of coordination and flexibilities are implemented. We conclude the work with a case study for a representative rural grid in Germany, in which we observe high economic potential in the flexible operation of buildings, majorly thanks to better integration of photovoltaics. Across all paradigms barring a best-case benchmark, grid reinforcement based on a mix of passive and active measures was necessary. A synergy effect is observed between flexibilities and coordination, as their combination reduces the peaks to the extent of completely avoiding grid reinforcement. The presented framework can be applied with a wide range of grid and component types to outline the broad landscape of future LV distribution grids. • Optimization framework for holistic planning of multi-modal LV distribution system. • Framework investigates grid reinforcement needs under flexibilities and coordination. • Framework is demonstrated with an exemplary rural distribution grid in Germany. • Synergy effects between flexibilities and coordination to integrate PV excess exist. • Flexibilities and coordination together reduce system costs by %25, and grid costs by 65%. [ABSTRACT FROM AUTHOR]