If you are not a professional photographer, and have no reason to use two cameras simultaneously, or have no critical reason to keep the 60D as an emergency backup (IE, expensive paying client!) Then I would totally suggest you sell that camera and pickup another nice lens for your 5DIII!!! Really I think this might be the way for you if your not actively shooting professionally. Investing in good L series glass is a better investment in the long run than holding onto a body you will rarely use. The only reason some of us professional photographers keep extra camera bodies is in the event of a camera emergency. Ive had cameras go down on me before. Rather than troubleshoot, I grab a backup body and worry about it later.
Ive got 2x5D3's, a 5D2, 7D, and even a 40D crammed in the back of my camera bag somewhere. The 5D2's and 7D are video cameras, the 5D3's my primary cameras. I always carry 2 bodies with different lenses for wedding photography.