This Project Syndicate post suggests a way European countries and the EU could deal with separatist movements legally.
If there was still demand for statehood and separation from the internationally recognized state to which they belong, the EU could invoke a code of conduct for secession. For example, the EU could stipulate that it will sanction an independence referendum if the regional government requesting it has already won an election on such a platform with an absolute majority of the voters. Moreover, the referendum should be held at least one year after the election, to allow for a proper, sober debate.
As for the new state, it should be obligated to maintain at least the same level of fiscal transfers as before. Rich Veneto could secede from Italy, for example, as long as it maintained its fiscal transfers to the South. Moreover, the new state should be prohibited from erecting new borders and be compelled to guarantee its residents the right to triple citizenship (new state, old state, and European).
The Catalonia crisis is a strong hint from history that Europe needs to develop a new type of sovereignty, one that strengthens cities and regions, dissolves national particularism, and upholds democratic norms. The immediate beneficiaries would be Catalans, the people of Northern Ireland, and maybe the Scots (who would in this manner snatch an opportunity out of the jaws of Brexit). But the longer-term beneficiary of this new type of sovereignty would be Europe as a whole. Imagining a pan-European democracy is the prerequisite for imagining a Europe worth saving.
I could almost imagine something like this in the U.S. No, there aren’t too many regions that would like to leave entirely, even if Texas makes noises about it. But my opinion is that the states are getting less and less relevant in an economic and practical sense relative to the metropolitan areas where the people live and the economic production happens, but they remain politically powerful relative to those metro areas. So I could see metro areas choosing to leave one state for another or seeking a legal and political status equivalent to a state. This would require a radical constitutional rewrite, of course.