Currently, the EP is a parliament of the nations. My gut reaction is that I personally can see a lot of value in adding some "transnational minority" seats, but there are probably philosophical implications that I haven't thought of. Of course, practical details would also need some hammering out.

Inside countries, it gets a little more complex. For example, in the UK, one might argue that the regional list system precludes any representation of minorities that are excluded from the major parties. (Who those minorities may be is for another comment.)

Instinctively I think it depends on the status of the minority in the country itself. One way to approach this is to ask "what's the status (and arrangements for) of the minority representation in the national parliament.)

Given the Finnish election system, it would thus be logical to suggest that an accepted principle of Swedish-language representation exists and it is in part the system used for EP elections that may change this and that deserves special legislation to fix.

However, by contrast, perhaps, the UK system offers no actual representation for non-geographically dominant minorities, so it's hard to argue they should introduce one there.

Coming back to where I started, I support the notion of "transnational minority seats" at least in concept because the Sami and the Roma clearly deserve some kind of representation, but it's very hard to make it happen through any of the national systems, due to their geographical spread.

One might wish that these groups were integrated enough into their countries not to need special representation, but I think that's pretty clearly not the case. Of course, that raises the issue of whether or not these "transnational seats" can be "set in stone" and I think it's where the concept does get into trouble. One can imagine and hope that the Roma will become much more integrated into various nations in 30 years time, at which point how do you then justify them holding any "transnational seats."