That was actually the point I was making, maybe badly worded. Rolls Royce were working on 2 stage Merlins long before the USA even entered the war, The Mustang Mk I. was arriving in UK before USA entered the war. For the USA to decide on handing Allison a research contract they would need a time traveller to tell them that what we know happened would happen in around 1940-41. Even if it could be done, in terms of US industry every 2 stage Allison engine produced would just replace a 2 stage Packard.This was NOT a question in WWII. If e could make a U.S.-built alternativer, then the decision would have been to do it. At the time, we were nothing if not nationalistic.
I don't think we would have done it simply because we were already making Merlins and there was no desire to spend development dollars to make up an Allison-designed 2-stage when the Merlin was already coming off the lines. I've seen a letter from Allison to the USAAF asking for funds to develop a 2-stage supercharger. It was declined ... the USAAF got exactly what it ordered. About the time the Allison was making really great horsepower, all the development money was going into jets anyway.