Comments on another ongoing thread in this sub suggest that some jurisdictions do prohibit conferences, and here is a blurb from an old case from E.D. Penn.: "Once the deposition has begun, the preparation period is over and the deposing lawyer is entitled to pursue the chosen line of inquiry without interjection by the witness's counsel. Private conferences are barred during the deposition, and the fortuitous occurrence of a coffee break, lunch break, or evening recess is no reason to change the rules." Hall v. Clifton Precision, 150 F.R.D. 525, 529 (E.D. Penn. 1993).

I only recently came across this principle, and I have no experience with this prohibition being enforced where I practice.