In the 70's Elvis was already doing a ton of amazing covers. I have a few live albums where he covers Unchained Melody, Bridge Over Troubled Water, You've Lost That Loving Feeling, and many more.
If he had lived I think he would do great versions of
U2 - Stay
U2 - Love Rescue Me
R.E.M. - Everybody Hurts
Bruce Springsteen - Drive All Night
John Mellencamp - Pink Houses
Van Halen - Hot for Teacher
Pearl Jam - Betterman