I'm not an expert with MS Exchange, but I'd say that what you are looking for isn't really possible.
Normally what one would do to save space on an Exchange Mailbox, is to move emails out of the Exchange Mailbox folder (.ost file) and into a Personal Folder or Achive Folder (.pst) file. The Personal Folder can't be shared in the same way that an Exchange Mailbox can, though. However, you could create copies of the .pst file, and send them to all 4 users who will load it into their Outlook, and they would all have access to the emails, but there would be no synchronisation accross all 4 users. You could then have 1 person update the .pst file, say every week, or every month, and then redistribute the .pst file. Keep current/new/recent emails inside your Exchange mailbox, and older ones you move into the .pst file, and redistribute to everyone for sharing.
Not ideal, lots of manual work, but it will work, and you all will still have access to all the emails (current/new/recent in the .ost file - Exchange Mailbox, and older files archived in a Personal folder - .pst file).
Hope this helps.
The best solution though is to get the IT Admin to just increase the size of your mailbox. If it is for work purposes, I can't understand why they would force you into so much difficult. IT systems are meant to make life easier, not harder. Unfortunately some people are just too thick or arrogant. Disk space is dirt cheap nowadays, so cheap that no IT department should be mising (mise-ing) about it for important work purposes...
UPDATE: Just re-read your post now (last read was long ago).
scenario: have a mailbox that currently 4 users share, but the mailbox needs to be cleared due the mail
admin not giving us more space on the exchange server.
So was thinking of implementing a .pst sort of a file that can be saved on a server and users access it simultaneously
This is a decent solution. It might work. But I believe that once the first person open's the shared .PST file, Outlook will lock the file, and nobody else will be able to access it until it is released. Unless of course there is a way to open up the file in Outlook in read-only mode....