Memory serves correct, all Allison V-1710 V-12 aircraft engines had at least one crank driven single stage single speed centrifugal supercharger. The Allison has only 6:1 compression, and without any supercharger at all would barely make 500HP.
Allison V-1710 engines without an EXTRA supercharger, such as the GE turbocharger on the P-38, were less than stellar performers over 15K.
The War Production Board and the USAAC/USAAF never saw fit to have a better supercharger installed on the Allison.
Were it to have been equipped with a two stage two speed supercharger, high altitude performance would have been roughly equal to the Rolls Royce/Packard Merlin series.
Of course, for many of the same reasons, it was almost always coupled to that crappy Curtiss Electric prop.