Here's a story idea to completely rewrite the Harry Potter series starting with book 1.
Instead of just Harry being born, he's just one of fraternal twins. Him, and his sister Rose.
In this case, there is no prophecy. Voldemort took advantage of Pureblood propaganda to style himself the Dark Lord and has done well for himself. Harry and Rose weren't targetted. Voldemort simply went after the Potters to take care of them himself after they defied him at least three times. A fidelius was still used due to it being prudent to protect themselves after defying him so much. Pettigrew still betrayed them. Sirius still went after the traitor and was captured.
Now here's where things get interesting!
Dumbledore USED to be Headmaster and chief warlock, but as soon as he became head of the ICW, the position forced him to drop all other positions to avoid conflict of interest since being head of the International Confederation of Wizards is a full time job, especially considering it's basically the Wizard version of the UN, with every single country, EVERY SINGLE ONE, having an insular wizarding community that must be represented. With Grindelwald being the world wide threat he was, everyone was happy to see Dumbledore become head of the ICW, but in so doing it required his entire focus, with him only able to dabble in backhome politics a little.
In place of him being Chief Warlock is Crouch, who quickly took advantage of the power void left behind when Dumbledore retired the position. With his hard stance against Death Eaters, once again Black was sent to Azkaban without a trial, only for Crouch to be 'forced' to retire when the debacle with his son came out. His replacement is (insert old fogie from the Wizengamot here).
As for Hogwarts, McGonagall was already being groomed as Head Mistress, and Filius took her place as Assistant headmaster. Not much else has changed in Hogwarts unfortunately thanks to pureblood propaganda and how badly muggleborn suffered during this time.
As for Harry and Rose Potter, with Dumbledore out of the picture, Hagrid never showed up. Instead Sirius saw to them being looked after for the moment by his sister Andromeda before he took off after Peter.
Thanks to that happening, and the court recognizing that with Sirius being the best claimant for the twins even with him being in prison, the Longbottoms stuck in St. Mungos due to being attacked, not for Neville being the other candidate for the nonexistent prophecy but because the Longbottoms and the Potters have long been friends so they'd still attempt to wrangle what the Potters did to end the Dark Lord out of them.
Speaking of, with no prophecy crap, the twins surviving the killing curse came even more out of left field than it already had. No one expected it. Not even Dumbledore. As for how Lily and James made it happen so their children could live, they took the secret to the grave. It certainly helped that Lily was secretly an unspeakable and tasked with studying the room that holds the 'love magic' in it though.
Anyway, with the Longbottoms unable to step in, the courts determining the Dursley's are extremely unfit to raise children (and incidentally the auror assigned to the case saw to the state looking into the family and getting Dudley out of their care before too much damage could be done.), and Sirius having the strongest claim despite being in Azkaban, custody was awarded to the Tonks since they were already looking after the two, and had already done well in raising their own daughter, Dora Tonks. (Yes, Dora. Not Nymphadora. I can't see a muggle father going along with such a ridiculous name, even if he is enchanted, figuratively, by the magical world.)
So the twins get a big sister who can change her hair color. Incidentally this starts Harry off doing the same thing to emulate his new big sister, while later on the family discovers little Rose hissing at garden snakes in the backyard. Thanks to the magic of being Twins, as Harry's metamorph talent grows Rose begins to be able to change her features subtly but not to the degree Harry can. Vice versa, Harry can listen and understand snakes, but he can't speak to them.
Raised in a simultaneously magic and muggle household, Harry grows close to his father and subsequently learns more about the muggle way of life thanks to that. Rose grows close to their mother and subsequently gains a more pureblood upbringing from Andromeda Tonks nee Black. That's not to say they're like night and day. It's like the bleedover from their abilities. Rose is just more proper than Harry with an interesting in politics, while Harry has a lot more injokes and a bit of a fascination with comics and technology. Rose wants to become Minister at some point while Harry's goal is to master technology and magic to the point that he can combine the two and advance the Magical World greatly, and do more than any other has before to destabilize the pureblood propaganda that muggles are lesser by doing so. (The power that Voldemort knows not. Technomancy! XD)
Meanwhile, Voldemort has been biding his strength in Albania. After 7 years, he begins a methodical hunt for the Flamels. Determining the stone to be in Gringotts, he breaks in, his mist like form very difficult to defend against since most of the Goblin's defenses are made to stand against those who have physical form since whoever heard of the need to defend against ghosts, or ghost like beings? They couldn't even pick up the gold and other valuables anyway!
The Flamels aren't stupid though. They catch on to Voldemort, or at least that some wraith is after the stone, and knowing it isn't safe there anymore, they contact Dumbledore in order to have him contact McGonagall in order to have the stone moved there. After all, what better to defend against a ghost like being than a castle full of ghosts?
Frustrated, Voldemort needs a way into the castle after the failure at Gringotts. Unfortunately he can't just go in the form he has, since he'd be noticed immediately. He has to smuggle his way in, preferably by possessing someone. Someone with a weak will who won't be able to fight him. Thus with his snooping, he finds about Quirrell, visits him in his home, possesses him carefully so even Quirrell won't know about him, and will work to enforce his will after he's through the Hogwarts wards and the immediate danger has passed. He does at least influence Quirrell to gain the DADA teaching position though. No way is Lord Voldemort going to put up with teaching Muggle Studies! After he's through, he'll take over completely. No living as a parasite for him, letting Quirrell destroy his opportunity to teach DADA, the one position he wanted in Hogwarts in the first place.
Oh, another note, neither Harry or Rose have the scar. Neither of them are an accidental Horcrux. In this story, there's no such thing. Making Horcruxes is a deliberate process, first with the murder to fracture the soul, then the ritual to pull the soul piece out of yourself and anchor it to an object. There's no such things as living Horcruxes either. In Nagini's case, Voldemort already had his six Horcruxes prepared. His sixth and last one he simply placed inside Nagini so that she would defend it with her life as extra protection, as well as lengthening her life, but with her death, Voldemort could simply move the Horcrux to the inside of another snake. Of course, Voldemort would have preferred Slytherin's Basilisk for this, but he never got the chance to return to Hogwarts after he left it with his schooling complete. So Nagini it is, his very own pet baby Basilisk.
With McGonagall agreeing to do this favor for Dumbledore and the Flamels, the Stone gets hidden in Hogwarts, only instead of it being a gauntlet created under the purview of Dumbledore, McGonagall isn't looking to lead anything into a trap that'll endanger the students. Thus she locks the stone in a box that is protected by Fidelius, which in turn is locked inside the hidden suite connected to the Headmistress' office. Between that and the army of Ghosts and other protections and wards of Hogwarts, Quirrelmort has his work cut out for him. Especially considering he only knows the stone is in Hogwarts and that's all he can know, along with anyone else. Circumventing that box is going to be tricky, let alone even figuring out the stone is in the box or that the box even exists. He's not stupid though, and he'll eventually jump ship from Quirrell to McGonagall to circumvent the issue of knowing the secret, even if she isn't the secret keeper. That's his last resort though, and won't happen until the end of the year while he does everything he can to figure out the secret and how to circumvent the fidelius without knowing who the secret keeper is.
In the meanwhile, the twins go to Hogwarts, making a big splash as the boy-and-girl-who-lived. An even bigger splash is when Harry gets sorted to Gryffindor and Rose gets sorted to Slytherin, but they debunk the rivalries and won't hear of anyone giving them crap about it, and so end up bridging the feud between the two houses slowly but surely. (Harry once again almost made Slytherin but thanks to Malfoy and a litany of begging went to Gryffindor instead where he would meet and become best friends with Hermione who would help him with his Technomancy goal. Rose wanted Ravenclaw so as to not be outted for being ambitious, plus Malfoy is a git, but she accepted her Slytherin placement from the hat, accepting that to achieve her dreams despite being outted as ambitious would be even more advantageous, especially as she used the Slytherin hierarchy to do it and thus turned the pureblood supremacy junk on its head in conjunction with Harry, plus there's the silver lining of getting to walk all over Malfoy as well. Her best friend ended up being Daphne Greengrass as the two became the Ice Princesses of Slytherin and the head of the up and coming power block in Slytherin, especially considering Rose, looking so much like her mother, soon had Snape wrapped around her little finger.)
Harry, having inherited his father's natural grace in the air, gains youngest seeker in a century once more, with Malfoy being even more of a git than usual since he views Harry as the more open target between the two, and takes advantage of this whenever possible. (Rose may have him by the metaphorical balls in the common room, but outside that, Malfoy is driven mad by being bested all the time by a female, the supposedly weaker gender.)
With Harry working, and steadily succeeding in making technology work around magic by converting the electrical circuits into runes, slowly a muggle revolution starts to take hold in Hogwarts. The boundaries between houses start to blur, and changes start to be seen in the school. When not being eaten in, the Great Hall starts being used as a study hall for friends to meet and work together on school work, or just hang out, the novelty of which is of course started by example by Harry Potter, who won't be separated from his sister for long as they grew up as best friends as well as Twins. Incidently, the Weasley Twins take their revolution as one massive prank and compete with them in what is pretty much a one sided prank war, since neither potter views pranks very highly, even with knowing their father liked pranks.
As for how the Twins and Quirrelmort end up clashing... I'm not sure about that part. I'm thinking Voldemort does something that arouses the suspicion, or Hermione researches the Sorcerer's Stone and the Potter Twins get involved that way, eventually figuring out like Voldemort, that it's in Hogwarts somewhere. Either way, things come to a head when Quirrelmort enacts his desperate attempt to gain the knowledge of the secret by possessing McGonagall. I'm thinking Rose witnesses this, and the twins confront him or something. I dunno. That's about as far as I've gotten with the idea.
That, and I figured if this is going to be a complete rewrite with only similar story elements, I figure this is the part where logic gets applied and the magic system gets retconned into something better, or Harry's muggle revolution will promote scientific experiments with magic resulting in the reclassification and study of magic being changed as we know it.
I'd write this out into a story myself, but knowing how I write, it'd never get finished. At least this way, seeing the synopsis like this, the story is pretty much finished and out of my head, so that's good enough for me. If it's not for someone else, and they want to flesh it out, go for it.