The question of data market compatibility across vastly different regulatory realms should be addressed well in advance of the need for such interoperability. Based on a thorough literature review, we develop an ownership-based approach to achieving institutional compatibility between data markets. We then modify the presently most elaborate regulatory proposal for a data market, the EU’s proposed Data Act, to comply with our institutional definition of markets to identify and evaluate the levers available for achieving data market compatibility, which we find to be the limitation of the scope of tradeable data and the prohibition of certain forms of use. We discuss our findings in view of the policy objectives of privacy protection and antitrust policy and conclude that an ownership-based approach is worth further investigation as it offers a viable and possibly more effective alternative to the present approach based on contract law and non-exclusive access and control rights.