This is insecure, because when you know some number and you know number/K, then you can calculate someone else's K.

But even if all parties could agree on some K and create such signatures, it is still not enough, because you can still calculate someone else's private key.

sA=(z+r*privKeyA)/(kValueA*kValueB)
sB=(z+r*privKeyB)/(kValueA*kValueB)
sA/sB=(z+r*privKeyA)/(z+r*privKeyB)
privKeyA=(sA/sB-z)/r
privKeyB=(sB/sA-z)/r

Everyone knows sA, sB, z and r, so everyone can calculate anyone private key if you use the same K in both signatures.