This paper develops multi-dimensional analyses of socio-spatial relations. Building on previous research, we identify some tensions associated with different dimensions of socio-spatiality and introduce the theme of compossible and, more importantly, incompossible socio-spatial configurations. Two short studies are deployed to highlight the socio-spatial implications of the principle that not everything that is possible is compossible. The first shows the power of thinking varieties of capitalism compossibly (via the concept of variegated capitalism) and then examines the successive strategies adopted by the European Communities and European Union to address the significance of changing patterns of variegation for approaches to European integration, spatial strategies, and economic and social policies. The second case discusses some related problems for state spatial projects, starting in the 1980s with spatial planning, promotion of a Europe of the Regions and/or of Europe and the regions, and then turns to examine city-regional development strategies.