Joe American graduates high school, joins the Army, serves for a couple of years, maybe a tour or two in Iraq, and is honorably discharged.
For reasons not germane to the thread, he winds up living in Canada. Could he join the Canadian Army?
It’s not completely unheard of here in the US.
This guy was in the British army, then in the US army.
I don’t see why not. Doesn’t every army have their own qualification standards? I don’t know if Canada requires Canadian citizenship for joining - does it? If he became a Canadian citizen, he probably could, assuming he fulfills age and fitness requirements.
I don’t think rank would automatically transfer, though. He’d need to be reappointed or recommissioned to his “old” rank specifically.
One of my ancestors served in the British Army (Black Watch) before emigrating to the US with his family - I don’t know if he ever served in the US Army or not.
Here’s another (more recent):
Wow. That is one hell of a guy.
A number of American soldiers who fought with distinction in Vietnam later volunteered for Rhodesia. Some even served in special units like the Grey’s Scouts.
I’ve known several former Israeli soldiers who had previously served in foreign armies, including a couple of American Vietnam War vets and a whole bunch of former Russian Army guys.
John Babcock served in the Canadian Expeditionary Force in World War I, and the US Army in World War II.
This guy was in the Royal Australian Navy and the Royal Australian Air Force before joining the Royal Navy.
My late brother-in-law served in the British Navy then moved to the U.S. and served in the American Navy.
I was going to say there were probably hundreds of WWII veterans who emigrated to Israel in the late forties and served in the Israeli military.
I’ve met several people who had served in the Soviet and other soviet-bloc militaries who moved to the US and joined the US military.
Lafayette Escadrille - Wikipedia (WW1)
Eagle Squadrons - Wikipedia (WW2)
American volunteers were formed into their own airforce squadrons under foreign (France & UK) service, and eventually, after America’s entry, transferred over to the US services.
Does that count for the OP?
Not just immigrants. Many thousands of Jews living in Palestine volunteered for the British military during WW2.
How about George Washington? He fought for the British during the French and Indian War, then later led a revolutionary Army against the British.
All the US Navy Sailors that were impressed by the British Navy in the years leading up to the War of 1812 probably qualify.
Drill Sergeant: “March! It’s aboot time you sorey little maggots learned some discipline, eh!”
Well, Benedict Arnold did! 
Many Irish people have served in both the Irish army and the British army.
And I would imagine that similarly many people have served in both the British military and in the military of one of the other Commonwealth realms. Even more so in WWI and WWII, when the distinctions between British nationality and Dominion nationality were quite fuzzy.
The grandfather of a friend of mine served in three or four armies, depending on your definitions - first in the Hungarian military, then in the British military during WW2, then in the Irgun (the right-wing Jewish organization) and finally in the IDF.
My best man did 10 years in the Irish army,then went and did a stint in the French Foreign Legion, basically just for the hell of it and for the bragging rights.