Problem with Requester List

Here is the scenario:

I have made 2 sites: Help Desk, and Engineering.
Both sites need to enter tickets for all the Company employees.
Currently all the company requesters are in the "not in any site" site.
The Help Desk and Engineering sites cannot view each other's tickets.

Here is the problem:

If I don't add the 'not in any site' group to the Engineering site, the engineers can only pick themselves as requesters.
If I add the 'not in any site' group to the Engineering site, they can see all requesters, but can also see the Help Desk tickets.

Is there a way that I can set this up, where each site can enter their own tickets for the company, and not see the other's tickets? I would imaging that this would be to add the requesters to both sites, but I am unsure if this is possible. Please help.