Spoilers below
I think it would be cool to see Chief descend into an unhealthy obsession with getting Cortana back. Not to the point where he is walking aimlessly muttering to himself all the time but a dark twist where he is in a sort of loneliness and lost feeling without Cortana. One of the reasons I really enjoyed this campaign is it felt more human. Everyone can relate to losing somebody (Cortana). It would be interesting if Chief ignored orders (This campaign showed he would ignore orders and maybe hints to more of that?)and went on a mad search to “find” or “save” Cortana. He would have all his focus on Cortana and would do anything to get her back even if it means jeopardizing his reputation with the UNSC.
Anyway, what do you guys think?