N.Y. Real Prop. Acts. Law § 916
Where the right, share and interest of a party has been ascertained, and the rights, shares or interests of the other parties as between themselves remain unascertained, an interlocutory judgment for a partition shall direct a partition as between the party whose share has been so determined and the other parties to the action. Where the rights, shares and interests of two or more parties have been thus ascertained and determined, the interlocutory judgment may also direct the partition among them of a part of the property proportionate to their aggregate shares. In either case, the court, from time to time, as the other rights, shares and interests are ascertained, may render an interlocutory judgment directing the partition, in like manner, of the remainder of the property. Where an interlocutory judgment is rendered in a case specified in this section, the court may direct the action to be severed, and final judgment to be rendered with respect to the portion of the property set apart to the parties whose rights, shares and interests are determined, leaving the action to proceed as against the other parties with respect to the remainder of the property; and if necessary, the court may direct that one of those parties be substituted as plaintiff.
N.Y. Real Prop. Acts. Law § 916