It is not proper to marry a woman and her sister, turning them into rivals of each other, for they should love one another and not be rivals (Ramban, Vayikra 18:18). Even if the law that “a convert is like a newborn child” applied before the giving of the Torah, it would not diminish the natural love between two converted sisters, which would be endangered by their sharing one husband.

We Learn the Law of Not Marrying Two Sisters from Ya’acov
The Torah contains various mitzvot that came about through events that happened to our forefathers. For example, the prohibition against eating the sinew of the thigh derives from Ya’acov’s battle with the angel (Bereishit 32:25-33). Rav Elchanan Samet suggests that the prohibition against marrying sisters may have come about through the events of Ya’acov’s life. Rachel and Leah were equally worthy of Ya’acov, and he needed to marry them both in order to build the House of Israel. Yet, the tragic rivalry that developed between them for the love of their husband and the rivalry over bearing children, described in Bereishit chapters 29-30 may have given rise to the Torah prohibition against marrying sisters. (http://etzion.org.il/en/prohibition-marrying-sisters). Nevertheless, Rachel and Leah were able to engender a tremendous rectification by overcoming jealousy. They refined themselves and reached perfection of character which paved the way for the ultimate unification between the segments of Israel. The Torah, however, cannot expect such high inner work from regular sisters.

The Mitzvot Pertains only to the Land of Israel
The Ramban is famous for teaching that the mitzvot apply only in the Land of Israel. Outside of Israel it is only practice. He explains that Ya’acov knew that the moment he entered the land, the prohibition against two sisters would apply: “G-d alone plans how things work out. Rachel died on the way, as they began entering the land. In her merit, she did not die outside Eretz Yisrael, and in his merit, he did not dwell in Eretz Yisrael married to two sisters, for she was married to him in contravention of the prohibition against marrying sisters. It appears that she fell pregnant with Binyamin before they reached Shechem; Ya’acov had no relations with her at all, within the land, because of the prohibition” (Ramban, Vayikra 18:25). “Ya’acov’s (true) intention in not burying Rachel in Me’arat Ha-Machpela was in order that two sisters would not be buried together, for he would thereby be embarrassed before his fathers” (Ramban, Bereishit 48:7). Ramban’s explanation does not go together with the Midrash quoted by Rashi, which says that Ya’acov kept all the mitzvot while living with Lavan. How could Ya’acov say that he kept the entire Torah when in fact he did not keep any of it, since he was not obligated in it while he lived in chutz la’aretz? However, we may say, based on the Nefesh HaChaim, that Ya’acov obeyed a specific command of G‑d, to build the Jewish people by raising the twelve tribes of Israel.

Personal Refinement Never at the Expense of Others
Ya’acov never intended to marry two sisters. Rather, it was brought about by Lavan. Since Ya’acov had promised to marry Rachel, not marrying her would have involved deception. Since the prohibition of deceiving applies to all humanity it overruled the command not to marry his wife’s sister, which had not yet commanded. Rabbi Schneerson of Lubavitch learns from Ya’acov’s marriage to Rachel that care for others overrides the concern for self-perfection that goes beyond G‑d’s law. When we desire to take upon ourselves more than G‑d demands of us, we must first make completely sure that we are not doing so at the expense of others.. (Likkutei Sichot, vol. 5, pp. 141–8). http://www.chabad.org/parshah/article_cdo/aid/101035/jewish/How-Could-Jacob-Marry-Two-Sisters.htm

The Unification of Sisters Rectifies Creation
The Zohar explains that the souls of Rachel, Leah, Zilpah, and Bilhah, were really four parts of one soul, called “Rachel.” The rectification of creation requires the reunification of all four parts into one soul. This is similar to how Ya’acov absorbed Esav into his being by first buying the birthright, and then receiving the blessings. The four holy wives of Ya’acov represent the four elements, the four primeval rivers in Eden, the four archangels, the four directions the four camps of the Shechina, and the four letters of Hashem’s name (Zohar Part 2, page 266b). Ya’acov’s mission in the world was to unify all these elements and thus rectify Adam, whose sin caused the fragmentation of the world. For the sake of this lofty rectification, Ya’acov had to deviate from heeding the command not to marry two sisters. His mission to rectify the split reality caused by Adam and Chava’s eating from the Tree of Knowledge of Good and Evil, by unifying the manifestations of existence, overrode the prohibition which had not yet been given. By joining together with one husband and overcoming the natural tendency of rivalry, Ya’acov’s four wives became as one unified person, enacting the highest tikun of creation.