The story might focus on how Hestia's values shape Harry. Hestia is associated with home and family, so Harry could grow up with a strong sense of family values. He might be more in tune with the importance of friendship as a form of family. Also, he could learn different magic from Hestia that is more related to protection and home - like spells to safeguard the places he loves. Maybe he would even use these skills to protect Hogwarts in a unique way later on.
One possibility could be that Hestia imparts her wisdom of the wizarding world to Harry in a very nurturing way. Since Hestia is the goddess of the hearth, she might create a warm and loving home environment for Harry, which is very different from his experience with the Dursleys. This could lead to Harry having a more stable emotional foundation as he grows up, and perhaps he would be less impulsive in his actions at Hogwarts.
Well, it could be a really interesting story. Raiden is from a different fictional universe, so he might bring some unique skills and values to raising Harry. Maybe he'd teach Harry some super combat skills like he has in his own world. Harry would probably grow up with a different kind of discipline and power control compared to what he would have learned at Hogwarts under the Dursleys and later at the school. It could also change his view on magic and how to use it for good in a more action - oriented way.
One possible storyline could be that Sebastian, with his own set of values and skills, trains Harry in a different form of magic. Maybe he emphasizes more on the practical and less - known aspects of magic. This could lead Harry to have a unique approach to dealing with threats in the wizarding world compared to his original upbringing.
Well, one possibility is that Harry would grow up with a different set of skills. Yoruichi is very agile and stealthy in her own universe. So Harry might be trained in those areas from a young age. He could be a master of movement and disguise, which would give him an edge in the wizarding world that others don't have.
Well, it could be that the Greek gods see Harry as a special being. They raise him on Mount Olympus. He would be taught by Athena in wisdom, so he'd be not only a powerful wizard but also extremely intelligent. His upbringing among the gods would give him a different perspective on good and evil. When he returns to the wizarding world, he'd use the values and powers he gained from the Greek gods to fight Voldemort. Maybe he'd use the gift of prophecy from Apollo to foresee Voldemort's moves.
One possibility is that Sirius would teach Harry all about his family's history in a more private and laid - back setting in France. He might introduce Harry to different magical cultures unique to France, like the Beauxbatons Academy. Harry could grow up with a more carefree attitude, away from the prying eyes of the British wizarding world.
Well, one possibility is that Harry would be trained in combat and stealth from a very young age, much like Damian Wayne was by Talia. He might grow up with a different view of magic, perhaps more as a tool for survival and power rather than just for study at Hogwarts. Also, his relationship with the wizarding world could be very different. Instead of being excited about Hogwarts, he might see it as a place full of naive wizards who don't understand the real world threats he's been raised to face.
One possible storyline could be that Bellatrix, despite her dark past, has a change of heart due to some magical influence or a deep - seated love for the Potter family. Sirius, of course, would be a positive influence. They might raise Harry in a more unorthodox way, teaching him both light and dark magic in a balanced way so he can understand the full spectrum. This could lead to Harry being a more powerful and empathetic wizard, able to bridge the gap between different magical factions.
The plot could involve Percy being raised away from the typical demigod chaos under Hestia's care. He may be trained in the ways of maintaining harmony and peace. Hestia could use her powers to shield Percy from some of the more dangerous aspects of the demigod world, and in turn, Percy might become a sort of ambassador for her values among the other demigods, promoting the importance of a stable home environment and the bonds that come with it.
Well, in this fanfiction scenario, Lily raising Harry would mean he'd be protected in a different way. Instead of the Dursleys' neglect, he'd have a nurturing environment. Lily could teach him about his father in a more personal way. Maybe he'd grow up with a stronger sense of family and heritage. Also, he might not have the same sort of scar - or it could be a mark of a different kind of magic, since the circumstances of his survival would be different.
He'd probably be more calm. Hestia's influence would likely make him less likely to jump into dangerous situations without thinking. He'd have a different view of family and might be more inclusive towards others, seeing them as part of his extended family.