The bottom end of the 4.4 will handle a supercharger without modification. The more you get out of a mod the greater the risk. You spend ya money and takes ya chances.

In addition to the supercharger you would need a matching tune, bigger injectors, high flow MAF and throttle body and to maximize benefits, lower restriction exhaust. Dinan offered a kit many years ago (no longer available) that took the 4.4 to 421HP and 404FT/LBs of torque. That kit also included the above and an intake manifold that had larger runners.

Turbos are more efficient and with twins there is very little lag. My research is dated but I found that good twin turbo kits and supercharger kits were about the same price. The supercharger kits are a less time consuming install so if you aren't DIYing labor install cost of turbos will be more. Other mods like lower ratio diffs are great values. I make my go fast decisions on dollars spent per HP/TQ improvement, focusing on improving 0-60 time. Due to weight of the X5 torque percent gains are more important than horsepower improvement.

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X5 4.6 2002 Black Sap, Black interior. 2013 X5M Melbourne Red, Bamboo interior
Dallas