(a) When defendant may bring in a third party. 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 thirdparty complaint not later than 10 days after serving the original answer. Otherwise, the thirdparty 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 counter-claims against the third-party plaintiff and cross-claims against other thirdparty 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 a 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 shall thereupon 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 and 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 thirdparty defendant for all or part of the claim made in the action against the third-party defendant.(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 the circumstances which under this Rule would entitle a defendant to do so.