N.Y. Civil Practice Law & Rules Section 1009
Claim by plaintiff against third-party defendant

1001
Necessary joinder of parties 1002
Permissive joinder of parties 1003
Nonjoinder and misjoinder of parties 1004
When joinder unnecessary 1006
Interpleader 1007
When third-party practice allowed 1008
Answer of third-party defendant 1009
Claim by plaintiff against third-party defendant 1010
Dismissal or separate trial of third-party complaint 1011
Successive third-party proceedings 1012
Intervention as of right 1013
Intervention by permission 1014
Proposed intervention pleading 1015
Substitution upon death 1016
Substitution of committee or conservator 1017
Substitution in case of receivership or dissolution of a corporation 1018
Substitution upon transfer of interest 1019
Substitution of public officers 1020
Substitution of indemnitors for executing or attaching officer 1021
Substitution procedure 1022
Substitution: extension of time for taking procedural steps 1023
Public body or officer described by official title 1024
Unknown parties 1025
Partnerships and unincorporated associations 1026
Review of determinations by administrative officers of the unified court system