I see 2 issues here.
1. Timely access for all users.
2. Data backup.
1. Normally for a file to be shared peer to peer one user opens the file and shares it to other users. Subsequent users need to use the Open Remote command to open the file. If the limited access user opens the file and you have subsequently opened it without using Open Remote that could be the cause of you being effectively locked out of the file. You are really opening the file as "read only" because it is already in use.
Solution: You will need to designate one user as the host and the others use Open Remote.
2. If your server volume and database file are backed up at any time when the database is open by a user you are exposing yourself to the risk of file corruption and loss of data.
The Best Solution: Get Filemaker server - it is designed to perform backups on live data files and can serve your database to multiple users whenever they need to access it.
Hope this helps
Shared network drives are NOT a good place to store FileMaker files that are shared with multiple users. Having the file on your local drive and opening it with FMP is actually a BETTER way to share the file between multiple users than the network share, but not as good as FMS.