The installation of infrastructures for carbon capture, transport, and storage to tackle the problem of CO2 emissions from European power plants and carbon intensive industries, is of strategic importance to reach future greenhouse gases reduction targets. However, the public reaction to the deployment of these technologies is still uncertain, and opposition may result in either cancellations or delays. This article provides quantitative insights into how social acceptance affects the design of a European CO2 infrastructure. A multi-objective mixed integer linear programming model is developed to optimise the design the entire supply chain, by simultaneously addressing the minimisation of the costs to install and operate the infrastructure and the maximisation of its community acceptance. The goal is to provide optimal supply chains in terms of costs, whilst considering the social behaviour of inhabitants towards the installation and operation of either CO2 pipelines or injection wells. Results demonstrate how the methodology may be exploited to assess the response of local communities and identify design strategies aiming at a trade-off between economic objectives and social acceptance. Although the maximisation of social acceptance leads to a +34% increase in costs with respect to the economic optimum, it is shown that an intermediate solution between the two objectives (i.e., economics against acceptance) entails a just slight increase of +8% with respect to the cost of the best economic configuration.