I know that a lot of people have requested the ability to share users and that this feature is not currently available. One way to approach this issue is through a database sychronization such as the Synk component. I run multiple sites and currently use that component. However, it can be a bit buggy at times depending on how much information has to be sychronized.

My proposed solution is this - and maybe it wouldn't work as I'm not a database expert. Is there any way to get the slave Joomla installs to only use a partial database and to draw the rest of the information from the master database?

For example, the things that you would want to be unique such as articles, modules, etc. Those tables would be drawn from the slave database. And then things that you would like to be universal, such as users, community builder, etc, would be drawn from the master database?

So instead of synchronizing the databases and having multiple copies of the information, you just have one copy on the master database for certain tables. It would be the same concept as the way the component works with the Joomla files, where each site can have its unique template, but the core files are shared.

Would this be a possible solution?

NO because the usage of the table prefix.
You can not have a part of a website that query some table using the table preifx of another website.

There is another approch that I will implement and I know how.
I just have no time for the moment before june because this require between 2 or 3 month of full time development.
This is planned.