Mobility should be at the core of the reallocation of taxing rights debate. With such a premise in mind, this contribution addresses this issue within Pillar One in its two components: the apportionment of taxing rights to market jurisdictions on residual profits of the most significant MNEs worldwide (Amount A) and the standardization of the remuneration of related party distributors that perform baseline marketing and distribution activities in market jurisdictions (Amount B). The aim is to show that not only the mobility of individuals but also that of MNE structures when deciding on their presence in market jurisdictions are relevant in building new paradigms on the allocation of taxing rights at a cross-border level through the specific impact of the said OECD proposal. Even if Pillar One seems doomed to fail, lessons learned from its design and its specific impact on mobility matters should inform further developments in reshaping international taxation.