Gear driven superchargers boost the intake pressure, and therefore can maintain that manifold pressure up to the critical altitude...that altitude at which full throttle is used.
TURBOsuperchargers do much the same, except that they are exhaust driven.
Several engines in the past have used both...the Boeing Stratocruiser comes to mind, using Pratt&Whitney R4360's.
Others include the B-29 and several models of the B-17.
However, so far as I know, only the Stratocruiser used both a supercharger AND a turbosupercharger, in civvy design.
However, the Boeing Stratoliner may well have been another.
And then we come to the superlative of piston engine design, the CurtisWright R3350 turbocompound engine, using both a two stage (speed)supercharger and power recovery turbines (3), which delivered BHP directly to the crankshaft, thru fluid couplings....not unlike the 'ole Buick Dynaflow idea.
More than you wanted to know, I expect...
