Official word is no, You need to calibrate for a 6 speed, Hard to get the GM dealer to agree to it.
Allisontech
There are two possible transmission that can be found in a 2001 Chevy Silverado 2500HD. The most common transmission is an Allison five-speed automatic transmission, which was meant for lighter workloads. However, the ZF six-speed manual transmission was also introduced as an option for heavier workloads.
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The 2001 Porsche Boxster has a 5-speed manual.
The 2001 Kia Rio has a 5-speed manual.
The 2001 Toyota Sienna has a 4-speed automatic.
The 2001 Audi TT has a 5-speed manual.
The 2001 Nissan Pathfinder has a 5-speed manual.
The 2001 Porsche 911 has a 6-speed manual.
The 2001 Lincoln Navigator has a 4-speed automatic.
The 2001 GMC Savana has a 4-speed automatic.
The 2001 Kia Sportage has a 4-speed automatic.