I went ahead and signed up for the add-on domain. When I go to Fantastico from my cpanel and click on Pro Edition (SohoLaunch) it says this:
Only one instance of this script can be installed!
You need to remove the existing installation in order to re-install."I don't want to remove anything. I understand that it says this because I'm using it on my main website.
I decided to leave Pro Edition and go to the Content management area. Looking through them I chose php WebSite. I clicked install and I'm to choose which domain I'd like it to be added to. Do I use myadd-onsite.my domain.com or just myadd-onsite.com? And into what directory? It seems that I wouldn't leave it blank because then it would try to install into the root directory of my main site.
Darn it Jim, I've confused myself. 