Hmm...I've been trying to figure this out too. If you listen to stuff like I'll Back You Up by DMB, Tim improvs some awesome chord shapes (after his solo, he does this arpeggio thing that is AWESOME behind Dave and his guitar).
I haven't listened to a lot of TR stuff, but from the DMB/D&T I've listened to, I've noticed a few patterns. In a lot of songs he uses a two-note chord, starting on the G with the root, and than the third on the B:
Major(C)- Minor(B)
E:-----------------
B:--5---------3----
G:--5---------4----
D:-----------------
A:-----------------
E:-----------------
I've just seen Tim do that a few times, so I thought I'd throw that out there...not sure if that's exactly what you're asking for, but I hope it helps lol.