In Tom Clancy's fictional "Rainbow Six" universe, customizable teams of special operatives use intelligence from around the world to strike at threats against NATO. Designated "Rainbow," the team was originally 30 members and is comprised of the best Delta, SAS, and other top NATO-member special operations units have to offer.
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Rainbow deploys on quick notice around the world, fulfilling both a deterrent and a direct action role, mostly against terrorists.
The real-world NATO must have seen all of this and — in light of recent Russian aggression — decided Rainbow just wasn't big and strong enough for the real world.
Instead, NATO announced in February the planned components of their Very High Readiness Joint Task Force. As part of the overall NATO Response Force, the VJTF does have special operators from around the world supporting it and an international intelligence network.
What units will make up the rest of the air component, as well as the exact forces in the maritime and special operations components, have not been announced.
Of course, the special operations support could be coming from Rainbow — if you believe the government is hiding an international special operations force from the American public.