How do I add additional links below the main menu link?
For instance, I might have menu link Categories then below that current and specials.
If we have understood you correctly you want some kind of Mega Dropdown Menu like these ones: http://vandelaydesign.com/blog/galleries/mega-menus/
The Categories Header Menu can be adjusted to work like a Mega Menu to some degree but it is not designed to be a Mega Menu and it will require some manual modifications to the view file.
We are planning to release a new Mega Dropdown Menu plugin for nopCommerce 2.4 that will have this functionality integrated and manageable from the Admin panel.
Hope this helps!