The techniques used in this paper can be applied to other matching problems with more complex constraints, such as hierarchical constraints or multi-dimensional constraints, by adapting the framework to accommodate these specific constraints. By incorporating the principles of stability, core, and blocking within the context of the given constraints, it is possible to analyze and derive optimal matching solutions that satisfy the constraints while ensuring stability and fairness. The key lies in understanding the underlying structure of the constraints, defining appropriate blocking criteria, and developing algorithms that can efficiently compute stable matchings within the given constraints. This approach can be extended to various domains where matching problems with intricate constraints arise, providing a systematic and effective way to address complex matching scenarios.