Well, one possible plot could be that Thor and Loki's little sister has some special powers that are a mix of their own. She might be caught in the middle of their feuds, trying to bring peace between them. For example, she could use her powers to stop Loki from his mischievous plans that would anger Thor, while also making Thor understand Loki's motives better.
The plot could involve her being kidnapped by an enemy of Asgard. Thor and Loki then have to put aside their differences and work together to rescue her. Along the way, they discover secrets about their sister that they never knew before, like she has a connection to an ancient Asgardian prophecy that could either save or doom their realm.
It could be Malekith. He might see the sister as a way to get to Thor and Loki and gain power over Asgard. Since she's a new and potentially vulnerable target, he could try to use her in his dark schemes.
In fanfiction, her character is distinct from Thor and Loki. Thor is associated with honor and strength in combat, Loki with his slyness and intelligence in manipulation. Their sister can be seen as a bridge between their two extremes. She may not be as physically strong as Thor but has her own form of power, perhaps in the realm of diplomacy or magic that is different from Loki's. For example, she could use her magic to create harmony rather than chaos like Loki. Also, her motivation might be different. Instead of Thor's quest for glory or Loki's desire for power, she could be driven by a need to protect her family and the realms in a more holistic way.
One common theme is envy. Loki may envy Thor's position, strength, and the love he receives from the people of Asgard. This envy can drive Loki to do things he might not otherwise do, like plot against Thor or try to prove himself in extreme ways.
One possible fanfiction could focus on Loki's struggle with always being in Thor's shadow. Since he is the little brother, he might feel overshadowed by Thor's popularity and heroic deeds. Loki could be trying to find his own identity and purpose, distinct from just being Thor's brother. This could lead to a story where he embarks on a solo adventure, facing challenges that force him to rely on his own wits and magic, rather than Thor's strength.
There are quite a few fanfictions out there. In some, she is a powerful sorceress like Loki. For example, in 'Sorceress Sister', she uses her magic to help Thor in battles against dark forces. Some fanfictions also explore her relationship with the other Asgardians. In 'Asgardian Bonds', she forms new alliances and friendships within the realm while also reconnecting with her brothers.
Thor might initially go into denial. He can't believe that Loki is truly gone. He may hold Loki's body for a long time, as if waiting for him to come back to life. Then, he could become angry. Angry at the situation, at whoever or whatever caused Loki's death. Eventually, he may find solace in the memories of Loki. Remembering the good times they had together and using those memories to move forward.
The plot could involve Thor being led to Loki's tree by a vision. He arrives there and discovers that the tree has some sort of magic that is tied to Loki's past or future. Maybe it holds the key to saving Loki from a great danger.
Maybe Loki is betrayed by someone he thought was a friend, and he is deeply hurt both physically and mentally. Thor discovers what has happened. He becomes extremely protective. He first takes care of Loki's wounds, using his own knowledge of healing herbs. Then he sets out to find the one who betrayed Loki. Along the way, Thor makes sure Loki feels safe and loved, constantly reassuring him that he will always be there for him. This journey not only heals Loki's physical and mental wounds but also deepens their brotherly bond.
In this fanfiction, perhaps Thor hits Loki with Mjolnir as a form of punishment for one of Loki's many tricks. Maybe Loki has double - crossed Thor in a plan to take over Asgard, and Thor's only option to stop him is to use his powerful hammer.
There's 'Thor's Redemption in Loki's Arms'. In this story, Thor realizes his true feelings for Loki after a series of events that nearly tear Asgard apart. It's a tale full of emotion and character development.