The issue of taxing the digitalized economy has revealed significant fault lines in the OECD’s Base Erosion and Profit Shifting (BEPS) Project, which aims to tackle tax avoidance by multinational corporations. Unilateral taxes that establish new taxable presences for digital companies are being rapidly proposed by several countries. Meanwhile both the EU and the US have contemplated tax reform proposals that would undo the long-standing separate entity approach embedded throughout the OECD recommendations. In this article, I combine a historical institutionalism approach with a multiple streams framework to explain why changes in the international tax regime have been incremental until BEPS and how problems associated with taxing the digital economy might open a window of opportunity for a fundamental path-departing agenda. Several EU state aid cases revealed an increased urgency for a solution on digital taxation, reopening the “problem stream” relatively soon after BEPS project was initiated. Meanwhile, because the United States shifted to a territorial tax system and digital economy as a specific issue was singled out the package deal of BEPS, the “political stream” and the negotiation stances of the EU and US are changed. These developments have created new dynamics in the “policy stream” as policy entrepreneurs in the EU and individual countries have proposed viable unilateral solutions, outside of the OECD recommendations, as an attempt to influence or bypass the OECD multilateral process. Evidence is drawn from policy document analysis and qualitative interviews with EU and OECD policy makers.