For the higher levels, I think it would be cool to be contacted by one of the other two governments, hinting that there would be benefits for you if you turned against your own government. This would result in a mission if you accept; and the completion of that mission would switch your faction from that of your current government allegiance to that of allegiance with the government which contacted you.

Also, I think Corvus or other corporations should be able to contact you, and that, by completing enough of their missions, you become a freelancer: neither UIT nor Itani nor Serco

Yes. This is a great idea and I've actually suggested it myself a while back. You would probably have to have a certain faction standing with the foreign government before the mission even became a possibility, and after you completed the mission the government you defected from would hate you.