Perhaps they live together because they both feel a bit out of place in the regular Gryffindor dormitory. They start a little project where they try to combine their magical skills. Harry's talent for Defense Against the Dark Arts and Neville's growing confidence in his own magic could lead to them developing new spells or magical techniques. They might also have a shared garden where Neville grows magical plants and Harry helps protect them from dark creatures that might be attracted to the powerful magic of the plants.
One possible plot could be that Harry and Neville discover a hidden chamber in Hogwarts that is full of ancient magical plants. Neville, with his love for Herbology, is excited and they both explore it. Along the way, they face some magical creatures protecting the plants and they have to use their combined skills of magic and Neville's knowledge of plants to get through. It could strengthen their friendship as they rely on each other.
One possible plot could be that in a world where the roles are a bit different due to fem Harry being female. She and Neville might bond over their shared experiences in the wizarding world, especially their fight against Voldemort. As they grow closer, they realize their feelings for each other and eventually get married, perhaps with a big wizarding wedding attended by all their friends from Hogwarts.
It could be some rogue Death Eaters who escaped justice. They might target Harry and Neville because they see them as a threat to their plans of a slow resurgence of the dark side. Since Harry is the Boy Who Lived and Neville was a key figure in the downfall of Voldemort, the Death Eaters would want revenge.
One possible plot could be that Harry, after years of dealing with the chaos in the wizarding world, decides to live by himself to find inner peace. He might choose a secluded place, like a small cottage deep in the Forbidden Forest. He spends his days studying ancient magic that he never had time for before, and perhaps he starts to document his past adventures in a detailed journal.
One possible plot could be that Harry and Fleur end up living together due to some post - war arrangements. They might initially have a bit of a cultural clash as Fleur is part - Veela and has her own French - influenced ways, while Harry is very much a product of the British wizarding world. But over time, they learn from each other and become friends. Harry could be teaching Fleur about some of the more unique aspects of Hogwarts' history that she might not know, and Fleur could be showing Harry some of the beautiful magic she learned in Beauxbatons.
One possible plot could be that Harry, for some reason, has to leave the Dursleys earlier than in the original story. The Greengrass family takes him in. Maybe Daphne Greengrass and Harry become friends and study magic together. They could also face some threats from the Dark side, and Harry's presence in the Greengrass family might put them in danger, but they all stand together to fight against it.
Well, perhaps the plot could be that Harry is on the run from some dark forces and the trunk becomes his only safe haven. He might have enchanted it to be much larger on the inside, like the Room of Requirement. Inside, he could have all his essentials, his school books, his owl, and a little bed. He uses magic to keep it hidden and moves from place to place without being detected.
Well, one possibility could be that Harry discovers a hidden magical island. He might find new magical creatures there and learn unique spells to survive. Maybe he builds his own little wizarding home on the island.
Perhaps there could be a plot where Sirius and Harry team up to uncover secrets about the Dark Arts that are hidden in the Black family home. As they explore the old rooms and artifacts, they might stumble upon a powerful and dangerous object that the Death Eaters are also after. This would lead to a race against time to either destroy or protect the object while also fending off the Death Eaters.
One possible plot could be that Harry is turned into an animal, like a stag, which is his Patronus. He then has to navigate the wizarding world in this new form. He might use his animal instincts to discover hidden secrets or evade his enemies. For example, he could sneak into places unnoticed as an animal, which he couldn't do as a human. He might also communicate with other magical animals in a way he never could before, and they could help him on his quests.