Everyone knows that wizarding children often take on an aspect of magic during their childhood. Innate specialties. Children of quidditch players might be able to fly without a broom for a time, those raised by fisherman might be able to manipulate water with great ease. Harry Potter comes to Hogwarts able to heal from any injury. At least he's got Tom keeping him company.
No one knows what happened that Halloween night, but Jack Potter is named the Boy-Who-Lived. But what will happen to his brother, Harry, when he is sent to the Dursleys for 'safety'. What will he become? Powerful, Intelligent, Grey Harry. 3 years older than Canon. Alive Potters, Good-but-manipulative Dumbledore, AU
What if Petunia wasn't so poisoned by her sister's magic, and when her orphaned nephew appeared on her doorstep chose to treat him as family rather than a burden? AU that will start pre-Hogwarts and get progressively further from canon
A Harry more affected by his childhood goes to Hogwarts, upsetting the chessmaster's plans as he does so. How will the Wizarding World react? Grey, Intelligent Harry; Manipulative Dumbledore; Pairing undecided but won't happen until 2nd/3rd year at least