In a nutshell, everyone (and that means everyone, top down) needs to clam up and shut up. No public statements, no tweeting, do not give an opening for anything. If a witness makes a big pre-testimony statement, they often can't take the fifth after that because they can be called to address the content of the statement. Witnesses often waive this right intentionally, by just answering the question, or unintentionally, by answering other questions that establish a basis on which they may be compelled to answer on the basis of rebuttal or further inquiry on the topic.
Shut up and clam up. Make the accusers prove their case, don't give them anything.