How to consider collaborators' time in reports?

How to consider collaborators' time in reports?

Good evening, dear community. Writing to you from Russia. 
Our company have ManageEngine HelpDesk. (If what ServiceDesk NOT PLUS (No servicedesk in categories))
System admins receive a salary directly proportional to the number of applications of Users.
But there is a problem. 
Let's say SuperDirector wants to open a new office. He writes to HelpDesk. First the application is accepted by a manager, who buys equipment.
Then he redirects an application to a man who buys a PC/Keyboard. And then this application is redirecting to sysadmin who install OS/Software.
Okay, this pc will go to the office. So sysadmin is closing the application.
When we want to see a reporn by this work, we can see that only sysadmin was a main figure, just because he closed the application.
We want to see total work of all specialists, but can't understand how to do it.
Help please!

if anything, we think to buy a license version. But can we do it in non-licensed version??

Thanks for watching and help! 

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