(b) Amendments to conform to the evidence. When issues not raised by the pleadings are tried by express or implied consent of the parties, they shall be treated in all respects as if they had been raised in the pleadings. Such amendment of the pleadings as may be necessary to cause them to conform to the evidence and to raise these issues may be made upon motion of any party at any time, even after judgment; but failure so to amend does not affect the result of the trial of these issues. If evidence is objected to at the trial on the ground that it is not within the issues made by the pleadings, the court may allow the pleadings to be amended and shall do so freely when the presentation of the merits of the action will be subserved thereby and the objecting party fails to satisfy the court that the admission of the evidence would prejudice him in maintaining his action or defense upon the merits. The court may grant a continuance to enable the objecting party to meet the evidence.
(c) Relation back of amendments. Whenever the claim or defense asserted in the amended pleading arises out of the conduct, transaction, or occurrence set forth or attempted to be set forth in the original pleading, the amendment relates back to the date of the original pleading. An amendment changing the party against whom a claim is asserted relates back to the date of the original pleadings if the foregoing provisions are satisfied, and if within the period provided by law for commencing the action against him the party to be brought in by amendment (1) has received such notice of the institution of the action that he will not be prejudiced in maintaining his defense on the merits, and (2) knew or should have known that, but for a mistake concerning the identity of the proper party, the action would have been brought against him.
(d) Supplemental pleadings. Upon motion of a party the court may, upon reasonable notice and upon such terms as are just, permit him to serve a supplemental pleading setting forth transactions or occurrences or events which have happened since the date of the pleading sought to be supplemented. Permission may be granted even though the original pleading is defective in its statement of a claim for relief or defense. If the court deems it advisable that the adverse party plead to the supplemental pleading, it shall so order, specifying the time therefor.