Yosef: Av or Shevet

The seforim discuss the idea that although Yosef was one of the 12 shevatim, he also had aspects in him that made him like one of the Avos. One rayah to this is that we see Yosef could have had 12 children of his own if not for the fact that 10 dops of shichvas zera left his fingers by the ma'aseh of Potifar's wife.

I have always wondered what would have happened if Yosef was zocheh to have 12 children. What would their role had been in klal yisroel? Would all 12 children been zocheh to be shevatim like Ephraim And Menashe eventually were? Also, by Ephraim and Menashe, even though they were shevatim, we still have only 12 shevatim since at times we remove Levi from the equation. If Yosef had 12 children how would we have counted the shevatim?

I'll leave it as a tzarich iyun for now.