In short, no, you can't.
Long answer, extension methods are just syntactic sugar. IE:
If you have an extension method on string let's say:
public static string SomeStringExtension(this string s)
{
//whatever..
}
When you then call it:
myString.SomeStringExtension();
The compiler just turns it into:
ExtensionClass.SomeStringExtension(myString);
So as you can see, there's no way to do that for static methods.
And another thing just dawned on me: what would really be the point of being able to add static methods on existing classes? You can just have your own helper class that does the same thing, so what's really the benefit in being able to do:
Bool.Parse(..)
vs.
Helper.ParseBool(..);
Doesn't really bring much to the table...