Apparently Weird Al covered a bazillion songs on his last tour. True covers, not parodies. A lot of the ones I listened to were pretty straightforward, so I don't know that he added or took away much from the songs. But still. It's Weird Al!
Anyway, you can check it out the whole list - 4+ hours of covers! - here:
And I suppose it's worth making note of this particular TMBG cover: