I need to put in yet another plug for Don Julin's 'Mandolin for Dummies' book. That chapter on Jethro's 3 finger chords is pure gold. Spend a couple of weeks with that and you'll have dozens of major, minor, and 7th chords all over the neck at your beck and call.
He also has a youtube on'Whiskey' out there which shows 3 different approaches to backup. It's more about rhythm, but he throws in a couple of fingering variations too. It's only about 6 minutes long and worth a view.
Edit. Found the clip I was thinking about: youtu.be/oUCHfqMXGCo . It does show the Em that Mike mentioned. And the form is actually one of the Jethro 3 chord fingerings. That particular form could actually become a 4 finger chord with a full barre, something I do, and I suspect everyone else coming to mandolin from a guitar background uses.