We study the existence of stable matchings when agents have choice correspondences instead of preference relations. We extend the framework of Chambers and Yenmez (2017) by weakening the Path Independence assumption. For many-to-many markets, we show that stable matchings exist when choice correspondences satisfy Substitutability and a new General Acyclicity condition. We provide a constructive proof using a Grow or Discard Algorithm that iteratively expands or eliminates contracts until a stron
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