The ways in which multinational companies operate in the current economic context questions the adequacy of international coordination of corporate taxation. A conceptual approach would require abandoning the classic paradigms of the international tax system (permanent establishment, arm's length, transfer pricing); they remain at the basis of the “Base Erosion and Profit Shifting” project (BEPS) elaborated by the OECD but are now obsolescent. The crisis of this system has been exacerbated by the Trump Reform and the explosion of the digital economy. The former introduces new regimes that undermine international cooperation and are in contrast with the WTO rules and with the double taxation treaties, regardless of the traditional OECD principles. The latter has features that cannot be governed by current tax rules, even if improved with the suggestions of the BEPS project. Solutions proposed at international level or applied by individual countries could lead to great uncertainty. A rational response to these challenges would rest on different bases, such as those of a system of formulary apportionment, with advantages in terms of simplicity, cost and certainty, fostering allocative efficiency and growth. Although this design is not feasible at international level, applying such a system in Europe, with the common consolidated corporate tax base (CCCTB), could ensure greater attractiveness and efficiency of the EU internal market: it would apply the same formulary system applied to other markets (e.g., the US market), while intra-European transactions are still regulated by the transfer pricing mechanism.