One idea and song that comes to mind is "I've Seen Fire and I've Seen Rain" by James Taylor. He plays it in D with a capo on the 3rd fret. The other guitar plays it in F without the capo (the key it is written in). So, even though you are playing the same chords, they sound different and you add a little bit of style differences based on the chords (e.g. D, Dsus2, Dsus4, etc). I'm sure there are many other songs that could be done like this.
You could also do "Duelling Banjos" on guitar.
HTH.
Nutty
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