Multi domains single database?

So, awhile back I asked about books or websites for learning to use Drupal. Learning Drupal by O'Reilly was high on the list. I bought that book. Now my problem was I only thought I had committed myself to learning Drupal. I started to use it and promptly was completely confused by user rights and taxonomy alone, much less the plethora of modules and trying to figure out which of those to use. Then if you happen to make it through that, there is the theme. I then started my path at trying every CMS that was even thought to be decent. Joomla, CMS Made Simple, E107, MODX, SilverStripe, Frog CMS, Wolf CMS, Plone, PHP Fusion, Xoops, Pimcore, Silex,and Wordpress. I am most positive that was not all of them, but I think most. Out of all of these only 2 have been able to keep my attention, Wordpress and Drupal. High in sight should have told me, if I had spent all that time messing with other CMS's learning Drupal instead I might be Ok at it by now. Seems I have been able to do most things I wanted in Wordpress much easier and quicker than in Drupal, but it seems no matter how I theme it, it still seems so Wordpress like. I threw a sample together in Wordpress and threw it out to the members of the non-profit organization I am a part of and trying to design this website for. They liked the functionality of it, mind you I am not a designer, but did not like the theme.

Since I have sufficiently illustrated how inept I am with Drupal, or any CMS as matter of fact, on to my question. With the response to the Wordpress sample was a list of ideas for functionality of the website, or as I found out as I read, a list of websites. This organization will now be a host to 3 performance groups. The members of all the performance groups are members of the organization. They are also all intertwined into all of the performance groups. So, we have members of the organization that perform in more than one of the performance groups. So, they would like to have, sometime in the future, a website to represent each performance group and one for the organization itself. That is 4 websites, but they also want to have a members only site for organization members. No registration will be available.

Their idea is to publish the 4 public sites using Wix, probably. Then just using a link or subdomain to push members to the Drupal(or other CMS) member site. Now it has to be said, most of the content for the Wix sites will be static except for the events, I suppose. Thing is, this means maintaining 5 different instances of websites, and 4 of them we can not even move the content to a different host. They will all have their own domain.

My idea is to let them use Wix as a design tool. Try to replicate, as best I can, the look of the websites with the theme of Drupal. Now, I know I only need one instance of Drupal and one database for the members site, but can I use this same instance of them for the static pages of the other sites using their own domains allowing me to maintain all of this in one place?

Phew, man, I am in way over my head. Way way over my head.

Thanks,
Richard