* Space Constraints: The engine bay of a C6 Z06 is relatively compact. Fitting a supercharger is challenging enough; adding twin turbos on top of that would require extensive modification, potentially including custom manifolds, intercooler placement, plumbing, and possibly even modifying the firewall or other structural components.
* Interference: The placement of various components (intake, alternator, power steering pump, etc.) would need careful consideration to avoid interference with the supercharger and turbos.
* Engine Management: The stock ECU would be completely overwhelmed. You'd need a sophisticated aftermarket engine management system (like a standalone ECU) capable of controlling the fuel delivery, ignition timing, and other parameters for both the supercharger and turbos. Proper tuning is absolutely critical to prevent engine damage.
* Complexity and Cost: This would be an incredibly complex and expensive undertaking. The labor costs alone would likely exceed the value of the car unless you're doing most of the work yourself (and have extensive mechanical and fabrication skills). You're looking at a significant investment in parts, custom fabrication, and professional tuning.
* Redundancy (and potential inefficiency): While technically possible, the combination of a supercharger and twin turbos is redundant and likely inefficient. Both systems are designed to increase airflow and boost, and using both simultaneously might create conflicting pressures and airflow patterns, reducing overall efficiency and possibly leading to instability.
In short: while technically feasible, adding both a supercharger and twin turbos to a 2008 Z06 is impractical, incredibly expensive, and likely to result in a poorly performing and unreliable engine unless handled by a highly skilled professional with extensive experience in forced induction modifications. Choosing one (supercharger or twin turbos) is far more sensible and achievable.