Master site, with differently themed "sub sites"

I have a client, that I am trying to determine a good solution for. I have done some Drupal work in the past, and also do quite a bit of custom PHP/MySQL work, so I'm not afraid to get my hands dirty.

What the customer wants is this-
They need a master site for the company, that contains all of the usual suspects- about us, contact, news, etc.. They want to be able to update the content on any of these pages, without worrying about screwing up the look and feel of the site (i.e.- edit just the textual content, be able to add a few inline images, etc..). They also want to be able to add press releases to a news page, with blurbs on their front page. Pretty simple stuff. I am confident that this will be simple to implement in Drupal (in fact, in one way or another, I have implemented all of these things in Drupal on other sites already).

Now where things become more difficult. The company currently has 4 product lines. Each line is quite distinct from the other- but each includes several different specific products. They basically want a "mini-site" for each product line, that has its own distinct theme. The overall layout of each "mini-site" would be the same, but with different coloring, branding, etc. Each site would have a overview page of the product line, as well as a page with more detail for each individual product in the line. In the coming few years, they can see adding between 2 to 4 product lines, and possibly dropping one or two existing lines. They want to be able to easily edit the images/information for each product line (they have a marketing person who is in charge of each), and want to be able to easily add new product lines, with the same general "mini-site" map and layout, but be able to apply a new theme/branding to the new lines. It also seems to me that I could use the users/groups functions to assign a specific person to have editing permissions for each individual mini-site.

It seems to me that if possible, Drupal would be a great solution, but the question remains: Is this something that is possible in Drupal? It seems to me that I might be able to set this up using taxonomy. Are there other modules I should look at? Would there be some custom work involved, or is this a "typical" thing Drupal can do? Any basic guidance would be greatly appreciated.