We have been doing multi-national excersizes here for decades. Red Flag in NV has had Eastern European aircraft along with our allies in the Empire (UK,NZ,Oz) for years. The Germany AF has a permenant base as part of Holloman AFB in NM.
We go overseas for excersizes in battalion/brigade strength too. Do the host nations consider us an invading army? (ok, some elements might) We have annual missions in Korea, Thialand, and all over Europe.