You could and I don't know for sure but I'd start with trying symbolic links from the ~/home to the public folder you want to use.
Then several instances of BC will try to write to the same files at the same time.
I don't think there's a straightforward solution to this.
Depends on what you mean with “multi user environment”. If it's a desktop or laptop shared by a family, it's impossible that two people are using it at the same time. Switching accounts may leave programs open, but (as far as I know) they get suspended and should not conflict with others. If it's a server (maybe like an online wallet), then definitely many people can use it, but in that case you should have a single program (other than Bitcoin Core) managing all accounts.