Calibre is single user system, so only one copy of Calibre can access the database at the same time (unless you want to corrupt the database).
There are basically two ways of sharing library:
- Use the Calibre Server option to access the library. This method allows multiple users to get at the books. In this solution a particular machine is running the Calibre server software
- use file sync software to copy calibre library files from the 'master' copy where books are updated to copies on other machines.