N.Y. Comp. Codes R. & Regs. tit. 22 § 202.29
In any civil action or proceeding, should counsel wish to proceed with a settlement conference before a justice or judge other than the justice or judge assigned to the case, counsel may jointly request that the assigned justice or judge grant such a separate settlement conference. The request may be made at any time in the litigation. Such request will be granted in the discretion of the justice or judge assigned to the case upon finding that such a separate settlement conference would be beneficial to the parties and the court and would further the interests of justice. If the request is granted, the assigned justice or judge shall make appropriate arrangements for the designation of a "settlement judge."
N.Y. Comp. Codes R. & Regs. Tit. 22 § 202.29