The EU’s Common European Data Space (CEDS) aims to create a single market for data-sharing in Europe, build trust among stakeholders, uphold European values, and benefit society. However, there is the possibility that the values of the EU and the benefits for the common good of European society may get overlooked for the economic benefits of organisations if norms and social values are not considered. We propose that the concept of “data commons” is relevant for defining openness versus enclosure of data in data spaces and is important when considering the balance and trade-off between individual (market) versus collective (societal) benefits from data-sharing within the CEDS. Commons are open-access resources governed by a group, either formally by regulation or informally by local customs. The application of the data commons to the CEDS would promote data-sharing for the “common good.” However, we propose that the data commons approach should be balanced with the market-based approach to CEDS in an inclusive hybrid data governance approach that meets material, price-driven interests, while stimulating collective learning in online networks to form social communities that offer participants a shared identity and social recognition.