Perhaps Kakashi time - travels and arrives at a point where he can stop Obito from making some of the more dangerous decisions that led to his downfall. He could also use his experience to train Obito and Rin better, making them stronger and more capable of facing the threats that were coming their way. This would completely rewrite the story and lead to a much different, and hopefully happier, outcome for all three of them.
In the fanfiction, Kakashi might travel back to a time when he can influence Obito's mindset more. He could show Obito a vision of the future that his actions would cause, which might deter Obito from going down the dark path. With Obito's change of heart, they could save Rin and form a more united front against their enemies. This would also mean that the Akatsuki might not form in the way it did in the original story, as Obito was a key figure in its creation.
One idea could be that Kakashi travels back to the moment right before Obito's 'death'. He uses his knowledge of future events to prevent the cave from collapsing on Obito. Then, together they are able to rescue Rin more effectively and change the whole tragic course of events.