The article aims at dusting the never-ending question concerning the borders between the different classical spheres of society (the State, the Market and Civil Society) off applying it to the domain of migration and asylum studies. Indeed, while reference to the important role of civil society actors is usually made by most of the literature about the local governance of migrations, the latter usually approaches the issue from a strict institutional and overtly optimistic conception of it, only rarely accounting for dimensions of conflict and power that should not be excluded from the analysis of governance mechanisms. To fill this gap, it is argued that civil society organisations (CSOs) frequently find themselves in dealing with a ‘civil dilemma’, i.e. the seldom win-win choice between the valorisation of their counter-hegemonic power vis-à-vis institutional policies and practices and/or the concrete and punctual satisfaction of asylum seekers and refugees’ contingent needs. Subsequently, it is argued that although the existence of dynamics of institutional governance should be refuted and a resistant modality of action on the part of CSOs recognised, their being reluctant about officialising the implicit inter-organisational relations among them hinders the collective organisation of a transformative pressure on the institutional interpretation of the responsibilities concerning reception, integration and multiculturalism. The article flows from a PhD thesis submitted in October 2020 and based on an extended period of participant observation within four different CSOs in Milan and through in-depth interviews to both CSOs’ members and asylum seekers and refugees turning to the latter.