Mysha, a 002223 will get you an A7 easier, although it'll sound different. And 000000 is Em11. ExxGBE gets you the Em. And an 11th has an extra 4th and 7th, which gets you A and D when your tonic is E.

For multiple thirds sounding good on guitar, it seems to be a case of finding the tonic - chords with multiple thirds where one is below the lowest occurence of the tonic seem to be unpleasant. C 032010 has three Es and sounds awful because of the low E honking out. Similar Em 322000 with a low G isn't great. But C x32010 has two Es and the tonic at the bottom holds it together, as does Em 022003 with two Gs. Similarly with G 320003 which has two Bs.

Although when you start fingerpicking and you're not playing the notes dead together, the same rules don't quite apply. Chords which would be hideous if played in one strum can be gorgeous when fingerpicked.

Graham.