Existing research on the transnational mobility of individuals tends to rely on limited and possibly misleading indicators. Arguing that mobility experiences are in fact multidimensional and cumulative over the course of a lifetime, this paper proposes a novel concept called ‘space-set’ and applies it to representative samples of the population in France, Germany and Italy (ELIPSS, GP.pop and Doxa surveys). A space-set is defined as the collection of each person’s geographical places known through first-hand experience. In a transnational perspective, its key dimensions are Size (the number of countries visited), Width (the farthest distance traveled), and Focus (being emotionally attached or not to more than one country). This new indicator measures individual-level inequalities of geographical mobility. As a proof of concept, the empirical part of the paper uses space-sets to address two research questions that loom large in different strands of the literature on social transnationalism: on the one hand, the social stratification of cross-border travel, on the other the association between transnational mobility and supranational orientations (i.e., cosmopolitan and pro-EU attitudes). Results confirm that space-sets are socially stratified by both class and education, and that larger, wider, and more transnationally oriented space-sets are associated with supranational orientations. Comparatively, all dimensions of space-sets are stronger in the German population than in their French and Italian counterparts.