The short answer is no, it is not within the competency of the EU Parliament to legislate on tax affairs, as that remains within the competency of member states, although the boundaries of that competency are being tested in the Apple Tax case where the Commission is suing Apple for back taxes worth €13 Billion - an action the Irish government is opposing even though it would be the main beneficiary. Apparently they are miffed that the integrity of the Irish tax authorities is being called into question.

In both the Apple and Microsoft cases the profits are generated by sales of intellectual property around the world and it is up to national governments to decide how they want to tax sales in their territories. The US threatened trade tariff retaliatory measures when the EU/France proposed a digital sales tax to do this.

The loophole that a company can be registered in Ireland without being tax resident here is currently being changed, which is perhaps why Microsoft channelled historic profits through here ahead of the deadline. The practice has been obscene, as you say.

Smaller countries like Ireland and Cyprus claim they need to set lower tax rates to compete with the bigger, more central members of the EU as otherwise all global corporates would HQ their EU operations in Germany or France. This wouldn't be so controversial if Ireland's 12.5% headline rate was actually the minimum rate applied, but as you say, further loopholes like the double Irish and Dutch sandwich have allowed some corporations to evade tax altogether.

The Irish government is resigned to a global minimal corporate tax rate being agreed at OECD level and that the days of extreme tax competition are numbered. Increased mandatory reporting of corporate profits at national level has also been recently agreed although opinion is divided on how effective it will actually be in increasing the tax take.

The Irish government doesn't have a problem with Biden's 15% global minimum corporate tax proposal and is expecting a drop in its tax take as companies are forced to declare profits where they are earned as part of the BEPS process. It's a case of "O Lord, let me be virtuous, but just not yet". The Augustinians have a long history in Ireland.

Index of Frank's Diaries

Yes but the question as to how long the EU has to put up with this disloyalty/cheating/corruption is very much open. I think the blackmail option, as currently being tried against Poland and Hungary over rule of law, is absolutely necessary and justified (you don't want EU common rules on tax? Well you want be wanting your various EU subsidies either...)
i.e. the rule of unanimity is not long for this world (or this Europe)

_{It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II}