How is it that Yaakov Avinu was permitted to marry Zilpah, because she was the sister of Bilhah and Leah already had 4 sons?
According to Bereishit Rabbah 74:13 Bilhah and Zilpah were also daughters of Lavan.
וַיַּעַן לָבָן וַיֹּאמֶר לְיַעֲקֹב הַבָּנוֹת בְּנֹתַי וְהַבָּנִים בָּנַי (בראשית לא, מג), אָמַר רַבִּי אָבִין כּוּלְּהוֹן בְּנוֹתָיו הָיוּ, הַבָּנוֹת בְּנֹתַי, הֲרֵי שְׁתַּיִם. (בראשית לא, מג): וְלִבְנֹתַי מָה אֶעֱשֶׂה, הֲרֵי אַרְבַּע. רַבָּנָן מַיְתֵי לָהּ מֵהָכָא (בראשית לא, נ): אִם תְּעַנֶּה אֶת בְּנֹתַי, הֲרֵי שְׁתַּיִם, (בראשית לא, נ): וְאִם תִּקַּח נָשִׁים עַל בְּנֹתַי, הֲרֵי אַרְבַּע.
"And Lavan spoke up and said to Ya'akov, 'The girls are my daughters, and the boys my sons.'" (Bereishit 31:43)
Said R. Avin, 'They were all his daughters: "The girls are my daughters" gives two, "And as for my daughters, what should I do?" (Bereishit 31:43) gives [another two equaling] four.'
The Rabbis brought it from here: "If you afflict my daughters" (Bereishit 31:50) gives two. "And if you take other wives in addition to my daughters" gives [another two equaling] four.
We can't say Bilha and Zilpah were from different mothers, as the midrash says they were actually twin sisters, just like Rochel and Leah.
We had been explained by Chazal already, that since Rochel was barren for many years, she relied on the actions of Sara, who took her handmaiden for the same reason, being barren, but Leah did not have that excuse as she had already given birth to 4 sons. We are also explained by Chazal why Yaakov was permitted to marry Rochel, the 2nd sister, because he had to keep his engagement vow to her, but once again, this does not apply in the case of Zilpah. As a matter of fact, after Zilpah becomes pregnant, Leah calls Yaakov "a Rebel" (בָּגַד) for betraying her!!
דָּבָר אַחֵר לָמָּה נִקְרֵאת תֵּבָה אַחַת בָּגָד, כְּמוֹ בָּגַדְתָּ בִּי, כְּשֶׁבָּאתָ אֶל שִׁפְחָתִי, כְּאִישׁ שֶׁבָּגַד בְּאֵשֶׁת נְעוּרִים:
Why is it read as one word? בָּגָד is like בָּגַדְתּ ָבִּי, you betrayed me when you came to my handmaid, as a man who has betrayed (בָּגַד) the wife of his youth.
Someone please explain to me why this is not a sin for Yaakov Avinu !?