Another fanfiction could be about Jon Snow (who is later revealed to be Ned Stark's son). In this story, he could fully embrace his Targaryen heritage much earlier. He might form an alliance with Daenerys not as an equal but as a leader, using his knowledge of the North and the loyalty of the Night's Watch to help her claim the Iron Throne in a more peaceful way.
A plot twist could be that Ned Stark's son Arya (disguised as a boy for most of her journey) is actually a secret weapon trained by the Faceless Men not just for personal vengeance but to be a political pawn. She could be used by some powerful force to manipulate the balance of power among the kingdoms.
One interesting storyline could be Ned Stark ruling justly in King's Landing. He might reform the corrupt systems in place. For example, he could ensure fair trials and end the excessive use of power by the nobles. This would likely earn him both respect and enemies among the powerful families. He could also focus on strengthening the city's defenses and improving the living conditions of the smallfolk, which would be a departure from the self - serving rule of many previous kings.
One simple way in fanfiction could be through some kind of magic. Maybe there's a powerful red priestess who discovers Ned's body before it's fully decomposed. She uses her magic to resurrect him, much like Thoros of Myr did with Beric Dondarrion. Once back, Ned could play a major role in the political games again, this time with more knowledge and a thirst for revenge against those who wronged him and his family.
One idea could be a fanfiction where Robert Baratheon's son, perhaps Joffrey (even though he was a cruel character), has a change of heart. In this fanfic, he could start to see the error of his ways after meeting a wise old maester who tells him tales of great but just kings. He then tries to make amends for his past actions, which would be a huge departure from his original character arc in the show and books.
Well, in fanfiction, the story could be about how Brandon Stark's son grows up in a post - Game of Thrones world. Maybe he has to deal with the remaining political unrest. He could be trained in the ways of the North, learning how to be a strong leader like his father.
In the fanfiction world, Ned Stark might kill Littlefinger if he discovers Littlefinger's true manipulative nature early on. Maybe he finds proof of Littlefinger's role in some of the political schemes that are endangering his family. Ned is an honorable man, and once he has evidence of such treachery, he would not hesitate to dispense justice.
It could be a northern girl, someone who Brandon met during his travels in the North. Maybe she was a daughter of a minor lord, and they fell in love while he was on a mission to secure the North's borders.
He'd become more politically astute. As a king, Ned would have to deal with the complex web of politics in King's Landing. He couldn't just rely on his sense of honor. He'd need to learn to play the game, which would be a big change from his straightforward nature in the North.
In a fanfiction, Robb Stark's twin brother might be a seer. He has visions of the future that are different from Bran's. While Robb is fighting his wars, his twin is trying to use his gift to prevent disasters. For example, he might see the Red Wedding in advance and try to warn Robb. However, due to the chaos of the war and disbelief from others, his warnings go unheeded. This could lead to a story full of regret and a new determination to avenge Robb's death and change the fate of the Stark family.
Another theme is sacrifice. Since they are in a dangerous world of 'Game of Thrones', they might have to sacrifice personal desires for the greater good. Fanfictions often show how they make tough choices regarding their family and the North.