Competitive equilibrium and stable allocation serve as pivotal benchmarks in addressing market design problems; however, they do not always exist. The absence of such solutions poses a major challenge, particularly in applications such as combinatorial auctions, resident matching with couples, and refugee matching with families. The primary challenges in these applications arise from the complementarities of preferences, where agents’ preferences over goods exhibit complex combinatorial independence. In this talk, I will introduce an approach that enables the reestablishment of competitive equilibrium and stable allocation by slightly relaxing resource constraints. The extent of relaxation aligns with the level of complementarity in preferences.