Wait until the EU tells them (funny enough that their own lawyers didn't tell them?) that they are required to name each party specifically and together with the specific purpose of their data sharing.
That's not what it's there for. It's not supposed to be a deterrent. The rule is there to be informative.
Think about what would happen if one of their partners was the police or the government. That would give them some pretty deep access that you may not want them to have.
That's not sufficient. For asking any kind of consent, the complete & specific info must be given before. Like "I agree to things that you have (probably, hopefully :-)) written somewhere else" - that is no consent.