Sure, that is possible, but this doesn't really have a lot to do with Plesk. Install a ticket system (Google around, there are lots of them) or write one yourself (a programming course is outside the scope of these forums I'm afraid).
If you want a ticket system, go find/buy/write one and install it. SWsoft sells a 'Multi-Level Help Desk' add-on for Plesk, but you can choose whatever software you like. Search for "ticket system" on Google and you will find a lot of ticket systems. I like OTRS myself.