As the most of you knows, there is an common modulus attack on RSA if all of them are encrypted with the same modulus (n=p*q), and different public exponents (e), but only if gcd (e1, e2)=1.
My question is there variations to apply this kind of attack if (e1, e2....en)<>1 ?

Only in some special cases maybe because AFAIK the attack is based on the Chinese remainder theorem.

that was a really interesting read

http://en.wikipedia.org/wiki/Chinese_remainder_theorem