One plot idea could be Harry discovering a new, ancient magic that gives him an extreme boost in power. He could use this power to reform the wizarding world's laws for the better. Another could be that Harry has a power transfer from an old, powerful wizard and has to learn to control it while facing new dark threats. Maybe he uses his newfound power to create a school for underprivileged young wizards and witches.
A plot might involve Harry having the power to time - travel at will. He could go back to key moments in wizarding history and change things for the good of the present. For example, he could prevent certain dark wizards from ever rising to power. Or, he could have the power of telepathy and be able to read the minds of all the Death Eaters, which would give him a huge advantage in the fight against the dark side.
Well, perhaps Harry gets a power that allows him to communicate with magical creatures on a deep level. He then unites all the magical creatures in the wizarding world, from house - elves to dragons, against a common enemy. He could also gain the power of super - speed, which he uses to quickly rescue those in danger during the chaos of a new dark wizard's attacks.