No need, everythings rosy
There's no need for restrictions on sharing. Every country in the EU is totally dedicated to the EU. They would never share information with outside powers in a way that would undermine the EU. No, never.
Tony Blair would never put George Bush above the EU, no sir.
Traian Băsescu of Romania loves the EU, there are no old loyalty to the old Russian empire in eastern Europe. None at all. Poland totally didn't set up secret CIA camps in violation of EU law. Nope, safe to send all your data to them. Everyone is completely committed to Europe and there is absolutely no need for checks and balances.
That's why everyone agreed on the EU constitution and nobody dissented and its why we all sing of our love of the EU each morning. "I pledge allegiance to the blue flag".