As microgrids evolve towards integrating diverse energy sources and accommodating interactive competition among various stakeholders, conventional centralized optimization methods encounter difficulties in addressing the game among multiple entities. Therefore, this study proposes a strategy to optimize the operation of multi-energy microgrids (MEMG) with shared energy storage based on a Stackelberg game. First, the system architecture is introduced, and operation optimization models are established for MEMG operator, user aggregator, and shared energy storage service provider, respectively. Second, the game relationship between MEMG operator and user aggregators is revealed, and a Stackelberg game framework is established considering shared energy storage between MEMG operator and user aggregator. Finally, the strategies of each entity were optimized based on a combination of heuristic algorithms and quadratic programming. Experimental results show the effectiveness of the Stackelberg game model, with the model proposed in this paper increases the revenue of user aggregator by 20.23%, and that of MEMG operator by 44.79%.