There is no reason they couldn't do that, they just need to write a good story. Then tie it up in a third film about the Forbidden land. Maybe That is where the X men have been (Ummm, X person? Thank you?)
I remember that from the comics. For a while Cap was working as a super spy for Shield, and worked with Black Widow. They got close and shared back story...
I am not Sure...but I believe that Nat was a product of the soviet super soldier effort, the "Red room" project was eugenics plus chemical/radio actives....???? Long time ago memories...