The EU members have not all signed up to the same agreements; for example, membership of the Schengen accord on border controls and membership of the Eurozone are both optional – as described in The Economist article cited above: Four Ds for Europe.
There is some pressure for EU reform. France’s president Macron argued, for example, in a speech on 26 September 2017 that the Eurozone should become more deeply integrated whilst other members need only comply with trading agreements; the speech was widely reported, as in The Guardian article entitled Macron lays out vision for ‘profound’ changes in post-Brexit EU.
It is possible to envisage MEPs for Eurozone countries being asked to vote on Eurozone matters whilst other MEPs would be asked to abstain. A more radical solution would be for membership of the European Parliament to be restricted to Eurozone countries; that would form a major part of political accountability for deeper political integration within the Eurozone – where political decisions on austerity, for example, would directly affect the lives of people living in those countries. Not all Eurozone members will want deeper integration, which would pass more powers to Brussels, but they are all affected by the European Central Bank’s decisions.
The question of political integration has to be resolved for Eurozone members, but seems threatening to those outside it. A two-speed structure would allow the EU to be politically repositioned as an inter-governmental organisation rather than having authority over member States – which is a much more accurate representation of what it is, for non-Eurozone countries.
It might be appropriate to have different budgets for the Eurozone, if it takes on more responsibilities. Non-Eurozone countries might then pay lower membership contributions.