If you have set-up your requests to come through a decicated project hosting the queue, I would suggest setting up separate project/queues for each group and control permissions/access via the project/queue permissions.
For example: I have a "test queue" I use to show future plans, do a quick test of some idea, etc. I give and take-away permissions based on who needs to see it, and it shows up as a separate choice during New Request depending on who has access.
Eventually, we plan to have a "report problem / feature request" request queue and will create another separate project/queue.