One possible goal could be to protect the wizarding world from new and unknown threats. Since Harry has always been a defender, his gang would follow suit. Another goal might be to promote unity among different wizarding groups. In the original series, there were some divides, but as a leader, Harry could aim to bridge those gaps through his gang.
Perhaps they aim to explore the uncharted parts of the wizarding world. There are many mysterious places that haven't been fully explored, and Harry's gang could be on a mission to discover new magical creatures, spells, or artifacts. They might also want to help younger wizards and witches who are having trouble at Hogwarts, like protecting them from bullies or helping them with their studies.
Harry's gang could include some of the characters we don't see much of in the original books. For example, the house - elves. Dobby was already very loyal to Harry. Maybe he could convince other house - elves to help out in a more active way. There could also be some of the older students who dropped out of Hogwarts for various reasons but still have a lot of magical knowledge. And of course, Hagrid could be an honorary member, providing his vast knowledge of magical creatures and his big - hearted support for Harry and the gang.
Well, he might have members with various magical abilities. For example, some could be excellent at defensive magic like Hermione, who could use her vast knowledge to protect the gang. There might also be those who are great at flying on broomsticks, like the Weasley twins, bringing speed and agility to the group. And perhaps some with a natural talent for dealing with magical creatures, which could be useful in different situations.
One possible plot could be that Harry, tired of the Ministry's inaction against dark wizards, forms his own gang. They could be a group that operates in the shadows, protecting the weak. For example, they might start by rescuing Muggle - borns who are being persecuted. Harry, using his skills and knowledge from Hogwarts, trains his gang members in defensive magic. They could also have a hideout, perhaps an abandoned wizarding house. Their main goal would be to bring justice to the wizarding world in their own way.
He might become more assertive. Normally, Harry is somewhat hesitant at times, but as a gang leader, he'd have to be quick in making decisions. For example, when facing an enemy attack, he can't afford to be indecisive.
Harry himself would be one of the main members, of course. Hermione could also be part of it, using her vast knowledge of magic to the gang's advantage. Neville might join too, having proven his courage time and time again. And perhaps some of the Weasley twins' friends from their pranking escapades.
In a fanfiction where Harry Potter joins a gang, it could lead to a whole new set of adventures. The gang might be involved in some underground wizarding activities, like illegal potion - making or trading in dark artifacts. Harry, being part of it, would be caught in a web of danger. He would have to navigate between his new 'friends' in the gang and his old friends from Hogwarts. This could create a great internal conflict within him as he tries to figure out who he really wants to be and what kind of wizard he wants to grow into.
If Harry Potter were raised by a gang in fanfiction, his values would likely be very different. He could be more cynical. Instead of the traditional Hogwarts values, he might value loyalty within the gang more. He'd also be more used to a rough - and - tumble lifestyle, which could make him a formidable wizard in combat as he'd be less afraid to get his hands dirty.
One more common theme is the struggle against dark forces. Even in fanfiction, the gang members often find themselves up against some form of evil. It could be a new dark wizard or a dark creature. They have to use their wits and magic to overcome these threats. Also, the theme of growing up is present. We see the characters evolving from mischievous students to more responsible young wizards as the story progresses.
In a 'Harry Potter Runs a Gang' fanfiction, Harry might run a gang that focuses on protecting the underprivileged in the wizarding world. His leadership would be based on his experiences with Voldemort. He'd probably have some rules that are different from the traditional Hogwarts rules. For example, they might operate outside the school grounds more often to help those who are being bullied by dark wizards. They could use magic in creative ways to outwit their opponents.
You'll often find Draco Malfoy in these fanfictions too. He could be the leader of a rival gang, with his Slytherin cronies. Neville Longbottom might also be a character, perhaps having transformed into a tough and resourceful member of a gang, using his knowledge of Herbology to create magical defenses for the gang. And of course, Dumbledore could be a sort of wise figure in the background, guiding Harry or other protagonists from afar.