Police Powers

I have an idea for a work, but it might contain rather a lot of legal complexity.

The basic idea is that an international corporation begins funding superheroes. The basic idea is that these superheroes are granted police power by the governments of multiple different nations, on the condition that there is reasonable oversight to their actions, making them effectively a special international police force managed by a private company.

What are some of the legal issues this would bring up? Is such a thing even possible? For the United States, each state might have to individually grant them police power, and they'd be subject to different regulations depending on the state, but I'm not sure.

You can look into how INTERPOL operates. My understanding is that it isn't its own police force but rather an organization for cooperation amongst various national police forces. Every federal country is different in the way it organizes its police. The US has federal marshalls to enforce federal law while general criminal law is under state jurisdiction and enforced by state or local police. In Canada, criminal law is all federal jurisdiction but police and enforcement is provincial. The Royal Canadian Mounted Police are a federal police force but they have no jurisdiction themselves. Instead, they are contracted by municipalities. Larger cities usually have their own police force while smaller ones will contract the RCMP or the provincial police.

Having said that, national security issues are always federal so you wouldn't have to deal with individual provinces or states. And most jurisdictions have citizens arrest laws. In Canada, anyone has the authority to arrest someone they catch in the act of committing a serious offence, or an offence related to their own property, or who they see fleeing from police.

Overall it would be a political mess with each country concerned about national sovereignty, immigration and customs issues and such. A country that entertained the idea of superheroes running about their land would probably want their own who are citizens themselves. Many would be loathe to ask outsiders for help unless they were facing a completely unstoppable menace.

There's the possibility that the superheros in other nations actually will be citizens of that particular host country, recruited through a regional headquarters of a corporation headed in America. The main reason they work for a corporation at all is that many of them don't have the Required Secondary Powers to be of much, or any use, but the corporation has developed technology to supplement these Required Secondary Powers.

Having things be a political mess, to a degree at least, is also part of the plan. The corporation winds up pissing off several nations, which leads to an entire new set of complications. They'd surely shut down any police authority that was once held. What sort of resources would the government have in terms of shutting down the corporation's operations in their country all together? Or reclaiming citizens who joined the corporation, and were involved in operations in America?