I have an idea for a diesel (and possibly any number of internal combustion engines).
Lets say you have a motor with a supercharger geared directly to the crankshaft, providing a fixed amount of boost throughout the rpm range.
Now imagine a blower that is attached not to the cranckshaft, but to an open differential; one output shaft to the blower, the other shaft going to do work.
At idle and other times which no load is placed on the motor, the blower gives nost boost (naturally aspirated).
As soon as load is placed on the motor, the work end rpms slows down, and a corresponding amount of rpms are added to the blower, instantly and automatically providing boost and therefore increased torque to overcome the load.
To make such a system works assumes that the load to drive the blower is always proportional to the output load and that won’t be the case. A high load that stalls the output would divert power to the blower. The blower may just inrease engine output until the whole thing blows up.
I liken it to a car stuck in the mud. The wheel with traction stops while the one in the sous spins ineffectually. The solution to that is a limited slip diff. Street racers used to weld the spider gear so it’s a solid connection, no more differential action AKA poor man’s posi traction. That’s pretty analagous to having a direct drive for blower and output.
There are so called torque sensing differentials like the Gleason that are supposed to direct output to the bigger load but I’m not sure there is any benefit.