* Complexity and Cost: Adding either a turbocharger or supercharger is a significant undertaking, requiring extensive modifications to the engine, intake, exhaust, fuel system, and often the cooling system. Doing both simultaneously dramatically increases this complexity and cost. You're looking at a very expensive and time-consuming project.
* Space Constraints: The engine bay of a Firebird, especially older models, is relatively cramped. Fitting both a turbocharger and a supercharger would require significant fabrication and potentially compromises to other components.
* Management Challenges: Controlling the boost pressure from both a turbocharger (pressure dependent on exhaust gas flow) and a supercharger (pressure dependent on engine speed) simultaneously requires sophisticated engine management systems (ECU tuning) far beyond a simple piggyback system. This requires specialized knowledge and tuning expertise.
* Diminishing Returns: While adding both might seem like a massive power increase, the gains are often not proportional to the effort and cost. The complexity often leads to tuning challenges and reliability issues. A well-tuned single turbo or supercharger setup usually yields better results for the investment.
* Stress on Engine Components: The increased power and stress on the engine from both forced induction systems will significantly increase wear and tear on various components, such as the connecting rods, pistons, and crankshaft. These parts would likely need upgrading to handle the added strain.
In short, while technically possible, adding both a turbocharger and a supercharger to a Firebird is impractical, extremely expensive, and likely to lead to more problems than benefits for most people. A well-executed single forced induction setup would be far more effective and efficient.