The condition that at least one B-preserving isomorphism is A-preserving is exactly the condition required by intermediate global supervenience.

It is easy to see that strong global supervenience entails intermediate global supervenience, which in turn entails weak global supervenience. If every B-preserving isomorphism between two worlds must itself be A-preserving, then if there are any B-preserving isomorphisms between two worlds at all, at least one of them must be A-preserving. So, strong global supervenience entails intermediate. And if at least one of any existing B-preserving isomorphisms between two worlds must itself be A-prese