with compound boosting (ie one blowing into the other), you have the big pressure ratio compressor followed by the small ratio compressor… so for the b8 s4, bug turbo blowing into small blower
it works on pressure ratios, so at 2k rpm the 1st stage may only make a 1.25:1 PR whereas the 2nd stage may make 2:1… total PR would be 1.25*2:1 or 2.5:1, hence the compund part.
at 6k rpm, now you may be at 3:1 on the 1st stage and 1.5:1 on the 2nd, compounded to 4.5:1 exceedly the reasonable limit of single stage compression.
the drawbacks are that the efficiencies also compound, and they are always less than 1. so if stage 1 at 6k rpm is 75% adiabatic eff and stage 2 is 70% eff, then your effective adiabatic eff is 52.5%, so thats a lot more heat. The nice thing is, you can intercool between stages to keep the air temperture reasonable (we have a 5000psi air compressor at my plant that outputs at 200*F)
you also will hurt reponse from low load to high load due to the extra piping, drawing through the compressor and pushing through the turbine
its typically best suited for where you have a motor that can handle more air than can reasonable be generated by 1 compressor. I have a few friends with 12v cummins with 2 & 3 turbos since they can handle 150psig of boost
main point of my rambling; if you feed the stock blower air at a high pressure its going to do the same thing it does to air at atmospheric pressure and bump it up in pressure by some ratio determined by the air the motor is consuming and the speed the rotors are spinning. the trouble may be that that air is much hotter than atmospheric