13th - isn't that what Prince used in "Kiss"? Try it up high, like 12th fret or so:
14
14
13
12
14
12
You can leave off the 2 low strings, especially if your middle and pinky aren't double-jointed. Interestingly then it lacks a root, you could make an argument for Dmaj11 rather than E13 in that case. Or switch to:
14
14
14
12
For a solid Dmaj7. Add a Ebmin7, as per raped by ape:
11
11
11
11
And pretty soon your records are being played on the Quiet Storm.