remove site from my site menu by user role

Have been searching around for an hour trying to figure out how to do this, but no luck so far. I have a multisite where users automatically become subscribers when signing up. I want to be able to remove the main site from the My Site menu, but not other sites as they will need to access their own. Any way to do this? Can't find any plugins so far, but maybe I'm using the wrong search terms.