Immigration has become a fundamental challenge for the European Union. Deep political divisions within and between member states make it difficult to find a common ground for effective cooperation. A solution could be a model of responsibility-sharing where countries are allowed to make different kinds of contributions to the collective good of migration governance in the form of sharing norms, money and people. To what extent can such a multi-dimensional approach overcome Europe’s divide on immigration and increase public support for European responsibility-sharing? Using original survey data across six EU member states, this article addresses this question in three steps. First, we map the preferences of European citizens on different dimensions of responsibility-sharing in European migration policy and identify the nature of the political divide. Second, we theorise and test whether these preferences follow a structural explanation of national interests or a political explanation of individual value orientation. Third, we estimate the level of common public support for different models of European responsibility-sharing. The results reveal that people-sharing is the most contested and least popular form of responsibility-sharing, and that multidimensional responsibility-sharing may not overcome the immigration divide but substantially increase aggregate support for European responsibility-sharing.