This paper studies many-to-one matching market in which each agent�s preferences not only depend on the institution that hires her, but also on her colleagues, that are matched to the same institution. With an unrestricted domain of preferences the non-emptyness of the core is not guaranteed. We present some conditions on agents� preferences, that determines two possible situations in which, at least, one stable allocation exists. The first one reflects real-life situations in which the agents are more worried about an acceptable set of colleagues that the frim hiring them. The second one is related to markets in which a workers� ranking is accepted by everyone (workers and firms) in the market.
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