The 3800 came equipped with two different superchargers from the factory. Each supercharger had a few changes over the years to make improvements.

At a high level the series 1 3800 was equipped with the smaller Eaton M62:

m62

The series 2 3800 was equiped with the larger Eaton M90 supercharger:

m90

In theory you can make any supercharger work on a 3800, the biggest thing to consider is the packaging around it. You will just need to make sure you can get the belt aligned properly and adapt it into the intake manifold correctly. It will also need ot fit into whatever vehicle you are using as well.

Here are a list of aftermarket superchargers that have been documented so far with links and images of such installs:

Eaton M112

Eaton M122

​​​Whipple

TVS1900
ford_gt