I'm actually writing something like this.

Is a combination of "Harry gets adopted by someone random" and "time/dimension-traveling MOD!Harry" story, but with a few twists.

My Dumbledore doesn't know that Harry is Harry the boy-who-lived. He is under the impression his little apprentice is his mentor, Nicolas Flamel, brilliant daughter.

He teaches her how to guilty trio people to get candy, look all knowing with ominous phrases and sneak on people to scare the hell out of them.

MOD!Harry is amnesic, and the last he/she remembers is Dudley hitting him with a golf club, and Vernon getting rid of his body in some forest. He knows spells, and stuff, but he can't remember anything about his life.

This, obviously, was Death's plan all along, because Harry was so miserable that even it fell bad for him, so it decides to give him a happy childhood.

Death couldn't prevent original Harry's (the original Harry have die, before MOD Harry could take possession of his body, but left some impressions, thus MoD only memories) accidental magic turning his master into a girl, though. So it decides to give Harry Bogart like powers.

Yeah, Bogart. Not metamorphmagus like, Bogart like. Harry can shapeshift on a whim and has the unccany ability what someone fears the most.

Dumbledore knows Harry is alive because "manipulate! Dumbledore device that looks like a trinket in his desk". And is searching for his, he really is. But he gets side tracked a lot thanks to little Jasmine (Harry) making puppy eyes and begging to take her with him in a new adventure.

For some strange reason she is almost always with him when he gets a new lead. (Obviously Death's doing)

I doesn't matter, though, he always has Severus following the same lead. (And ending up in really unfortunate situations.)