@JonesieAtJMP, did you make any progress on supressing it?
@Jeff_Perkinson, I think I have this resolved. Private Groups should only show up in the menu for those with explicit permission to that top-level category. I've created a component, currently in use on the home page at stage, that will display my company group, if you belong to one. I've tested this with three different scenarios:
1. Logged in as admin (my default profile)
2. Logged in as a user with explicit permission to the P&G group
3. Not logged in
It seems to work as expected with these three different scenarios, but you may have others that you want to test. Let me know if you see any issues.
I'm still seeing the menu when logged in as a user without access to a private support space.
You can impersonate jperkmac2 to see it.