Well, I’m just a country lawyer, but methinks that the key is to have he deposition/examinations in private, but conducted simultaneously for Clinton, Mills and Sullivan, and perhaps a few others. If they are done in private or public in serial fashion, with time for the previous deponent or examinee (or their lawyers) to transmit the answers to the next scheduled witness, then they have the opportunity to coordinate their stories.
Most Congressional committee investigations are conducted in exactly that fashion, for the reason stated.
Depositions in private first, public testimony later. The first an attempt to find out the acts off the matter, the latter an attempt to tell the story in a coherent fashion.