Interestingly, Midrash assigns a portion to Asnat equal to that of each of the male tribal heads of Israel:
Gen. 43:24–34 relates that Joseph invited his brothers to eat with him when they went down to Egypt to procure food. In the midrashic depiction, this was a family meal in which Joseph’s wife and children also participated. Joseph sat his brothers before him, “from the oldest in the order of his seniority to the youngest in the order of his youth” (v. 33), and brought the portions to the meal. Joseph gave each one, including Benjamin, his portion, and then he took his own portion and gave it to Benjamin. Asenath took her portion and gave it to Benjamin, as did Ephraim and Manasseh. Thus, there were five portions next to Benjamin, as is recorded in v. 34: “But Benjamin’s portion was five times that of anyone else” (Tanhuma, Vayigash 4).
Asnat (as the granddaughter of Jacob and a nameless woman) has an equal portion (of Israel) in her own right distinct from the portions of her husband, her sons and Joseph's brothers. Asnat has inherited what Leah may have feared a son of Dinah's mother (Asnat's mother's mother) may have inherited after all.