You can run any LinkFixer Advanced process on multiple machines at the same time, as long as you are pointing all instances of LinkFixer Advanced to the same database on your SQL server.

The Cure process is no exception. 

However, there is one additional step you should take when running Cure on multiple instances. You should enable the setting to "Pause after scanning files", as shown below.

This setting causes LinkFixer Advanced to pause after scanning files during the Cure process. 

The point of this "pause" is to allow all of your instances to complete the scanning step of the Cure process before any instance starts the step of matching links with child files and rewriting the links. It is important to let all instances complete the scanning of all of the files in their new locations before curing any of the links. Otherwise, some child files could be "missing" from the database when LinkFixer Advanced attempts to cure the links that point to those files.

After you enable the setting shown above, LinkFixer Advanced will pause after the Scan portion of the Cure process, and will present a dialog box with the option to "continue". Ensure that all instances have completed the Scan step, and are showing the dialog box, before you click {Continue} on any instance.

This additional step will allow LinkFixer Advanced to have all of the available data with which to complete the Cure process successfully.