Italy is the second largest extra-virgin olive oil (EVOO) producer within the European Union. Despite its importance in preserving rural landscape and in supporting household economy, the EVOO sector faces several constraints due to high management costs, small farm size, lack of cooperation and investment, production vulnerability, and farmers’ ageing. Such a number of weak points suggests the need to identify and adopt innovative approaches, at both the farm and oil mill levels. In order to address these priorities, a fuzzy cognitive mapping (FCM) survey was carried out in Umbria region, central Italy, involving key local stakeholders of the EVOO value chain in the Orvieto district. Based on stakeholders’ perception and knowledge, this paper aims to identify and evaluate the most relevant components of the local olive oil value chain, and predict scenarios responding to hypothetical changes of the same components. These stakeholders were firstly invited to each build an individual fuzzy cognitive map and then, grouped all together, build a joint fuzzy cognitive map. Finally, the maps represented both the individual and the grouped stakeholders’ perceptions. The maps were translated into adjacency matrices in order to create an FCM model by applying the software “Mental Modeler”. In total, 24 participants, including practitioners, multipliers, researchers, suppliers and members of local administration, participated in the survey. The component analysis and the scenario analysis highlighted several priority issues: to preserve the ecosystem functioning, to implement cooperation, innovation and education, to adapt and mitigate climate change. The main novelty of this study is that all stakeholders’ categories in the EVOO sector recognize several challenges to sustain the EVOO value chain, in particular, climate change adaptation and mitigation.