Most auto turbo engines have a fuel pressure regulator tied to the manifold pressure. So, up goes the boost, up goes the fuel pressure, and more fuel goes in. This is the simplest way, others using MAF adjust injector duty cycle in realtime or fire secondary injectors with increasing pressure. The Lotus is sort of a combination, having a fuel pressure increase and secondary injectors too. But, saddled with the old GM computer it uses it isn't very accurate nor flexible so the result is a very rich motor and lost power.
There are multistage compressor engines from the 30s and 40s - aircraft, auto, and marine. There are examples of two and three turbo stages along with examples of mechanical supercharger augmented by a exhaust driven turbocharger. Lots of neat stuff, but somewhat complex for auto use though.
I've always been intrigued by the possibility of using a Lysholm screw type supercharger in conjunction with a turbocharger. The screw blower provides instant boost, as long as its displacement is an appreciable fraction of the engine, and the turbo charger could be used to pick up the very high RPM range where you don't wish to drive the blower. It'd require some valving in the intake department that could be complex. One way would be to provide a relief valve for the blower that vents to atmosphere thus unloading it and at the same time closing a valve from the vented turbo allowing it to pressurize the manifold. Not sure what to do about a MAF system like this, would likely need a mapped system. Bet it wouldn't pay off in the end, but would be cool.
R