At any time after commencement of the action a defending party, as a third-party plaintiff, may cause a summons and complaint to be served upon a person not a party to the action who is or may be liable to the third-party plaintiff for all or part of the plaintiff's claim against the third-party plaintiff. The third-party plaintiff need not obtain leave to make the service if the third-party plaintiff files the third-party complaint not later than 10 days after serving the original answer. Otherwise the third-party plaintiff must obtain leave on motion upon notice to all parties to the action. The person served with the summons and third-party complaint, hereinafter called the third-party defendant, shall make any defenses to the third-party plaintiff's claim as provided in Rule 12 and any counterclaims against the third-party plaintiff and cross-claims against other third-party defendants as provided in Rule 13. The third-party defendant may assert against the plaintiff any defenses which the third-party plaintiff has to the plaintiff's claim. The third-party defendant may also assert any claim against the plaintiff arising out of the transaction or occurrence that is the subject matter of the plaintiff's claim against the third-party plaintiff. The plaintiff may assert any claim against the third-party defendant arising out of the transaction or occurrence that is the subject matter of the plaintiff's claim against the third-party plaintiff, and the third-party defendant thereupon shall assert any defenses as provided in Rule 12 and any counterclaims and cross-claims as provided in Rule 13. Any party may move to strike the third-party claim, or for its severance or separate trial. A third-party defendant may proceed under this rule against any person not a party to the action who is or may be liable to the third-party defendant for all or part of the claim made in the action against the third-party defendant. The third-party complaint, if within the admiralty and maritime jurisdiction, may be in rem against a vessel, cargo, or other property subject to admiralty or maritime process in rem, in which case references in this rule to the summons include the warrant of arrest, and references to the third-party plaintiff or defendant include, where appropriate, a person who asserts a right under Supplemental Rule C(6)(b)(i) in the property arrested.
(b) When Plaintiff May Bring in Third Party.
When a counterclaim is asserted against a plaintiff, the plaintiff may cause a third party to be brought in under circumstances which under this rule would entitle a defendant to do so.
(c) Admiralty and Maritime Claims.
When a plaintiff asserts an admiralty or maritime claim within the meaning of Rule 9(h), the defendant or person who asserts a right under Supplemental Rule C(6)(a)(i), as a third-party plaintiff, may bring in a third-party defendant who may be wholly or partly liable, either to the plaintiff or to the third-party plaintiff, by way of remedy over, contribution, or otherwise on account of the same transaction, occurrence, or series of transactions or occurrences. In such a case the third-party plaintiff may also demand judgment against the third-party defendant in favor of the plaintiff, in which event the third-party defendant shall make any defenses to the claim of the plaintiff as well as to that of the third-party plaintiff in the manner provided in Rule 12 and the action shall proceed as if the plaintiff had commenced it against the third-party defendant as well as the third-party plaintiff.