First you need to have the toolbox parts folder copied over to the network shared drive.
Next you need to modify the toolbox.ini file on every users machine and update the path to point to the new toolbox parts folder.
Then in order for multiple users to be able to use the parts at the same time you need to make some changes to everyones toolbox browser configuration.
What you need to do is make a change everyones toolbox browser to make them insert their parts as read-only...
From the toolbox dropdown menu, click on "browser configuration". The go to "document properties"...
Make the follwing changes to the configuration on each users installation:
Set these areas of this dialog box as follows:
In the "copy part" region set "NO COPY (always use master part file)"
In the "read only status" area set "INSERT AS READ ONLY"
In the "writing to read-only documents" area set "ALWAYS CHANGE READ-ONLY STATUS OF DOCUMENT BEFORE WRITING"
This will allow multiple users to access toolbox at the same time.