There was a well-worn precedent for that. During World War One, while Woodrow Wilson was promising to keep us out of war, the French fielded Escadrille N. 124, the Escadrille de La Fayette. It's pilots were Americans.
They weren't the only unit in the Great War like that. Perhaps the most famous one was the Czech Legion, made up of Czech and Slovak volunteers who fought at first on the Eastern Front, and then fought their way across Siberia to Vladivostok so they could be taken to France, after the Russian Revolution broke out, to rejoin the Allied effort.
Ukraine is taking in foreign volunteers for the Ukrainian Legion. However, much more here could be done along the same lines as the AVG. The AVG, basically, took in American military pilots used to American military gear, with that gear purchased for Nationalist China through an arrangement with the US.
This could be done in the war in Ukraine on a ground combat basis.
The US military was traditionally quite small before World War Two. From 1947 through 1990, however, it was very large due to the Cold War, and it's not been inconsequential in size since that time. The youngest of the Cold War warriors are now 52 years old, not young. But maybe not as old, in modern terms, as it might seem. At any rate, there are thousands of Americans in their 30s, 40s, and 50s who have served in the U.S. military.
Those men trained to fight the Soviet Union. And they used, in many cases, late Cold War and early post Cold War US equipment.
This isn't unique to the U.S. Germany only ended universal conscription of men n 2011. France in 1996. Thousands of men have served in the various NATO armies, using NATO standard equipment.
Why not create an American Volunteer Group and a European Volunteer Group and allow Ukraine to equip them with NATO standard weapons? There's more than enough old NATO equipment, surely, to equip two divisions in this fashion.
Would they be elite? Well, probably not, but they wouldn't be bad. Some have actually trained to fight the very war that's being fought right now.
And then there's pilots and aircraft.
Lots of men trained to fly high test American fighters are now flying commercial jet liners. Ukraine has asked for F-16s. Why not give them the F-16s with volunteer pilots?
And, we might at this point, why not include A-10s?