You are actually taking the wrong assumptions in your arguments dealing with the system including both supercharging and turbocharging on the Lancia delta s4. Neither one of the supercharger or the turbocharger totally "drives" the other one, this is a strange solution according to me, as one will always be restricting the other, unregarding in what order they are placed in the charging system. Easily proven that one too.

The supercharger on the s4 was an abarth construction based on the rooter-type of superchargers.

What the quite clever engineers at lancia/abarth did was too make two individual parallell pressure systems, one for the supercharger and one for the turbocharger, using the boost generated by the supercharger to help drive the turbocharger at really low boosts. The systems were linked together just before the intake-plenum via a special valve which controlled when, at what boost that is, too shut down the supercharger, leaving the engine as a "simple" turbocharged one. This valve was then controlled via the ECU. Other valves are also needed to perform this effectively, as information. Properly balanced and mapped, this created an engine characteristic which provided the optimal case of boost through the entire register of the engine. This is the optimal case of compound charging using a supercharger and a turbocharger, regarding performance.

The engine partly constructed by the native of mine, hilmersson, is roughly based on the same principle as described above...