The author addresses the phenomenon of taxable profit-shifting operations undertaken by multinationals in response to countries competing for corporate tax bases within the European Union. The central question is whether this might be a relic of the past when the European Commission’s proposal for a Council Directive on a Common Consolidated Corporate Tax Base sees the light of day. Or would the EU-wide corporate tax system provide incentives for multinationals to pursue artificial tax base-shifting practices within the EU, potentially invigorating the risk of undue governmental tax competition responses? The author’s tentative answer on the potential for artificial base shifting and undue tax competition is in the affirmative. Today, the issue of harmful tax competition within the EU seems to have been pushed back as a result of the soft law approaches that were initiated in the late 1990s and early 2000s. But things might change if the CCCTB proposal as currently drafted enters into force. There may be a risk that substantial parts of the EU tax base would instantly become mobile as of that day. As the EU Member States at that time seem to have only a single tool available to respond to this – the tax rate – that may perhaps initiate an undesirable race for the EU tax base, at least theoretically.