One answer to this question is found in Carl v, Cohen,  NY Slip Op 31747(u), a decision by Justice Edmead.  Here defendants Joel Cohen and Greenberg Traurig, LLP reached a "so ordered" stipulation concerning depositions of subsequent attorneys, against whom, presumably, defendants would either like to bring a third-party action, or to say that these subsequent attorneys could have saved the day, and who had a "last clear-chance."  Depending on that stipulation, which concerned depositions of the subsequent attorneys, defendants Cohen and Greenberg Traurig asked Justice Edmead to hold off on other depositions.  Defendants argued that a motion on whether the attorney-client privilege would be invaded be held off in view of the stipulation.

The Court acknowledged that there was indeed a stipulation, but determined that it could decide the motion, and that because plaintiff was willing to authenticate documents, that no deposition of the subsequent attorneys was necessary.  Accordingly, defendant’s attorneys will not get to ask the subsequent successor attorneys any questions.