I have a pet project I periodically come back at with a EU-funded counterpart to Delta Green, where operatives are agents of various national organizations (e.g. local police forces, intelligence, militaries etc) or super-national orgs (e.g. Europol, Interpol, although these usually do not have actual jurisdiction nor power of arrest). It's true that different countries have no actual power over each others territories, but they also often collaborate on cross-borders operations. It would not be weird for a Spanish detective to be working a case in Paris together with an Italian carabiniere, under the badge of a French gendarme.

Access to weapons is actually an interesting push towards being creative in finding unofficial ways of arming themselves, but I wouldn't stress it too much. We might not have handguns for sale near the pasta isle at the supermarket, but it's not like we don't have gunshops.