I had once mistakenly had one multitasking MySQL user handing three separate sites and their respective databases all at once, but I would think you would need some kind of router to have multiple users doing simultaneous traffic with a common database. Too many cooks stirring one pot, you know? I do know it is possible (and I have this) to have your own phpMyAdmin installed in a subfolder at your site, so maybe do that and then do some hard-testing just to see whether you can break something before going any farther.
http://kb.siteground.com/how_to_access_phpmyadmin_directly_from_my_domain/
note: you will see a couple of messages at the bottom of the screen. One goes away by making a config file from the sample file provided, and the other can go away by adding a database for some whistles and bells.