We show that generalized median stable matchings exist in many-to-many matching markets when contracts are strong substitutes and satisfy the law of aggregate demand.
Chen, P., Egesdal, M., Pycia, M., & Yenmez, M. B. (2016). Median stable matchings in two-sided markets. Games and Economic Behavior, 97, 64–69. https://doi.org/10.1016/j.geb.2016.03.004