<p>There's something I want to customize in the System.Web.Script.Services.ScriptHandlerFactory and other .NET stuff inside an internal class.  Unfortunately, it's an internal class.  What options do I have when trying to customize a method in this class?</p>

You might find
this recent article
enlightening.  Basically, it says that you can't override anything marked
```
internal
```
, and the source is about as authoritative as it gets.  Best you can hope for is an extension method.