The P-38 had both crankshaft driven superchargers, which were standard equipment on the V-1710 Allison V-12 engines, and turbochargers. The two stage single speed centrifugal supercharger driven by the crankshaft was an integral part of the engine. The General Electric B series turbocharger was added by Lockheed to compensate for the Allison supercharger being a single speed unit, and as such, unable to compensate for decreased air density at high altitude.
It was possible to equip the Allison with a two speed two stage supercharger, it just wasn't done. Just another mistake by a barely functional War Production Board. Had the Allison been so equipped, it would have been a perfectly competent high altitude engine without a turbocharger, although, like the Merlin, above a specific critical altitude, power would have dropped dramatically. Where the critical altitude occurs depends upon the gear ratio in the supercharger drive. That is why/how specific Merlin engines were tuned for particular altitude ranges. The turbocharger allows an engine to hold the same power to any altitude, so long as the turbocharger has sufficient size to supply the required air without exceeding its own RPM limit. For the General Electric turbochargers used on the P-38 and P-47, the critical RPM limit was reached at around 33,000 feet.
On the P-38, the turbochargers fed the superchargers, which is standard operating procedure for engines that use both a supercharger and a turbocharger. This was even done on heavy truck diesel engines, the Detroit Diesel 8V92 TTA engine was equipped with a crank driven supercharger (found on almost all of the old Detroit Diesel two stroke diesel engines) which is in fact the basis for the "blowers" (6-71, 8-71, 10-71, and 12-71, the "14-71" is a purely racing unit) you see on hotrod engines. The numbers in "8V92" designate the engine size, a V8 with 92 cubic inches per cylinder, which had an appropriately sized crank driven supercharger, also designated 8V92. The TTA suffix denoted twin tubochargers, and an aftercooler, also known as an intercooler. So you had a 736 cubic inch diesel engine with two turbochargers, feeding a supercharger through an intercooler. The same configuration has been used in racing. It is rather complex, but if the correct balance is achieved, massive amounts of power can be made.