I'm just a US speaker, so I can't explain the grammar, but I can explain the meaning. In this case, "possibly" strengthens the meaning.
"Could not" is just a little vague. It can mean what it says. It can also mean "usually could not" or "probably could not." "Could not possibly" makes it unambiguous.
"Leon Bagrit could not have foreseen the development of the Internet."
"Really? Are you sure? Vannevar Bush wrote 'As We May Think' in 1945."
"No, that was just speculation, almost science fiction. Leon Bagrit could not possibly have foreseen the development of the Internet, not by any stretch of his imagination."
"With the amount of money he had, he could not buy a house. And he could not possibly buy the kind of house he needed."