O I see. This is a challenge job, I think; and this could be possible happened anytime, moreover in a big company with many departments with also many staffs in there.
Since the ticket that has been created will be oriented to classified departments, it seems hard to make this happen, unless if you implement true Help Topic whereas osTicket version 1.6 RC4 has not implemented this, yet.
Fortunately, I have already done MOD for implementing Help Topic. You can search my post/thread that I started about this.
Assuming that Help Topic is a part of Departments, or, let's say in one Department, you may have some Help Topics, which is one staff will be assigned to one specified Help Topic, I think you can make it happen.
I wish I could fulfil your request, but I cannot promise you. I'm trying to make it come true... or perhaps somebody has already done this MOD? ;)
Best regards,
Masino Sinaga