I'm have Icecast running on my Linux machine. It can have multiple streams running at once.
https://icecast.org/

I found this that may help setting up multiple instances of Icecast to allow each user to have unique login details.
https://icecast.imux.net/viewtopic.php?t=6721

I'm not really clued up enough to provide much more detail. Though I know one user/instance can have multiple streams running simply by starting each stream with a unique mount point.

I only have one Icecast server running, but if I login from my Mixxx DJ program from multiple machines and give each one a unique mount point in the DJ program they will both be listenable on the same port. The URL's are identical apart from the last part which can be anything you specify as the mount point in the DJ program. So for example on one machine the mount is /stream and the other machine the mount is /stream2
The URL to listen is the same apart from the end which is either /stream or /stream2.

I assume if you setup multiple instances then each instance can have have unique login details, but would need to be on separate ports.

I often wondered how those stream rental places in SL automatically generate a username and password on the fly. I assume they have some lsl script that talks to their server and has another script that configures the icecast server automatically and passes the randomly generated login details back in world.

Sorry I can't be more helpful.