(a) When defendant may bring in 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 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 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 third-party 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.