Our starting point is a critical re-examination of (1) Marx's analysis of the socialization of labor in a capitalist mode of production and the mobilization of the capital minimum for the realization of new projects of competing capitalist owners (especially in the form of the joint stock company) and (2) Luxemburg's, Hilferding‘s, and Lenin's arguments on the functions and structures of corporations or "monopoly associations“. On this basis, we go on to explain, first, those changes of the agencies of capital accumulation which have taken place since Marx's times, as well as the modifications of the processes of the accumulation of capital this has brought about. Second, we go on to analyse the connections existing between the accumulation processes of the most powerful singular capital groups and the development of the EU with its treaties/economic legislation and its European and global role. Then (3), we discuss consequences to be drawn from this analysis of the present conjuncture for a realistic discussion on socio-political alternatives in the perspective of a strategy of socialist transformation politics. In this context, we improve upon the notions we had developed so far (a) of the intersectionality of societal hierarchies and power relations, on the one hand, and (b) of on-going and possible emancipatory struggles, on the other hand. In this context we also take up the discussion about emerging or already ongoing left-wing campaigns like "UN Treaty", "Change finance" and "Lobby control".