Enable the ability to turn-off/edit the “dongle“ on the C360 that allows direct access to SFDC objects

Not all customers want direct access to the Account, Contacts, and Opportunities from the C360 page. I would find it helpful if you could edit the objects that have a direct access link or turn this button off completely. 
In broader scope this can be handle by having different views of C360 page.
Hi Brent, Now this usecase can be achieved  by Multiple layouts(Admin>>CS360 Layouts)