Multiple domains with a blog on a subdirectory for each domain

I need to set some blogs up (details below) and I am currently considering several options, including WordPress. Given the scattering of information through the documentation wiki and plug-ins docs, as well as vague information about plug-ins, searching doesn’t seem to bring up any clear answer.

The server setup is somewhat typical: many domains residing as virtual hosts on a single LAMP server. Blogs would be needed for some of those domains, let’s call them “domain1.com”, “domain2.com”, all the way to 14 or 15 domains (and planning to add a few more soon).

The requirements I aim to fulfill are these:

• Single installation: dealing with 14+ separate installations would be just too much.
• Each blog should have a url in the form https://www.domain1.com/blog/. There is content within each domain that will remain there (ie: the blogs are an addition, not a replacement, to what’s on the sites).
• It would be preferable, but not essential, to have a single users table throughout the blogs.
• The blogs should use “beautified” URLs (a.k.a. permalinks). Using blog/.htaccess is ok, but using the file at the domain’s root is not an option (it’s already under heavy use and automatically updated by some scripts).
• I have full root access on the server that hosts these domains; and I am familiar (although not a guru) on most configuration aspects (in fact, I took care of installing the system and setting most things up from scratch).

I have two questions:
Can this be achieved with a minimal (no plugins) installation?
If not, what would be the minimum set of plugins required?