What does the Torah mean when it writes that "also the sons of Machir ben Menasheh were born on the knees of Yosef"?
Rashi and Targum Onkelos: The Torah means that they were raised on his knees.
Targum Yonasan: It means that he circumcised them. 1
Rashbam: Bnei Machir means grandsons (of Menashe, i.e. the fourth generation after Yosef). 2
Moshav Zekenim: Even though Yaakov did not bless Menasheh like (i.e. as much as) he blessed Efrayim, Hashem blessed Menasheh, and Yosef saw grandsons also from Menasheh.
Or that he was the Sandek at the Bris (See Perush Na'ar Yonasan).
Even so, Efrayim's children multiplied more than Menasheh's, as Yaakov had promised (see above, Bereishis 48:19). See also Ibn Ezra. Hadar Zekenim and Moshav Zekenim disagree. Yosef saw a fourth generation from Efrayim, and only a third from Menasheh (even though Menasheh was older; like Yaakov's Berachah "Achiv ha'Katon Yigdal Mimenu" (48:19) - Malbim).
What is the Chidush that Yosef saw a fourth generation? He lived to 110 years old. Even a man of 90 can see this!
Moshav Zekenim: It was a Chidush that all of them were alive. Not one of them had died.
Hadar Zekenim: He saw a fourth generation counting from Efrayim. 1
Malbim: The verse teaches that a man's mercy on his sons is until the fourth 2 generation - "Poked Avon Avos Al... Ribe'im" (Shemos 20:5).
This is a Chidush, for Yosef did not marry until he was 30, and initially there were very few girls for his sons to marry. Presumably, he would want them to marry descendants of Yaakov, and not Mitzriyos. Among Yoredei Mitzrayim were 67 males, and only two single females who might have married Yosef's sons, Serach and Dinah (and Dinah was much older than they, and some say that she married Shimon or Iyov)! Refer to 46:26:1:2. (PF)
Rashi (Bereishis 21:23, from Bereishis Rabah 54:2) learns from "Im Tishkor... ul'Nechdi" that it is until the third generation! This requires investigation. (PF)
Why does the Torah single out Bnei Machir alongside Bnei Efrayim? Parshas Pinchas implies that Machir was Menasheh's only son!
Ha'amek Davar: "L'Machir Bechor Menasheh" (Yehoshua 17:1) implies that he had also other sons, but they were not distinguished and worthy enough to be mentioned by name. They were swallowed into Mishpachas ha'Machiri. Also Yosef did not esteem them, so they were not born on his knees; only Bnei Machir were. 1 All of Bnei Efrayim was esteemed, and Yosef was happy to see sons from them.
Harchev Davar: Bnei Machir includes some of Bnei Yehudah - "v'Achar Ba Chetzron El Bas Machir Avi Gil'ad... v'Hu Ben Shishim Shanah, va'Teled Lo Es Seguv; U'Seguv Holid Es Ya'ir" (Divrei ha'Yamim I 2:21-22). Bereishis Rabah 98:8 expounds "u'Mechokek mi'Bein Raglav" (49:10) that Machir prostrated between Chetzron's legs, that he marry Machir's daughter, in order to beget lawmakers. Chetzron descended to Egypt when Yosef was 39, so Seguv was born "Al Birkei Yosef" before Yosef was 100, and grew up among Bnei Menasheh. I.e. in Yosef's old age, he cherished Ba'alei Torah and strove to marry into them. Yechezkel's Nevu'ah (Yechezkel 37) of combining Etz Yehudah and Etz Yosef was after the 10 tribes and Malchus Yosef ceased! Rather, it refers to the power of Torah in Yehudah, and of Chesed in Yosef.