Accidental Twin Acquisition
Battle at the Ministry, Bella hits Sirius with a spell, but before he can fall through the veil, someone comes shooting out of it. Chaos ensues when it turns out it is another Harry Potter, only this one is a Girl.
Harry (male) canon
Harriet (female, alternate universe) divergence from canon summer before third year, the accidental magic reversal squad catches Vernon beating her near to death after the Marge incident. Dumbledore pulls the magical guardian card and gets her placed with Snape.
This version of HP learned to trust Snape (but only him), was encouraged to actually try her best in her studies instead of slacking off like Ron, or pretending to be dumb to make Hermione feel better. She was vigorously trained by Snape when her name came out of the goblet in her 4th year, so she managed to survive the incident in the graveyard and delt the resurrected dark Lord a mortal blow, once more disencorporating him. Unfortunately, Crouch Jr escaped, and brought him back again near the end of her fifth year.
Snape never went back to spy, instead, he worked out how to remove his mark (so he wouldn't get tortured with it) with Harriett's help, using parseltongue and a modified magical adoption ritual.
In her 6th year, Dumbledore decides to start "training" her by showing her memories of Tom Riddle as a kid and his awful family and then his magpie tendencies. Snape helps her figure out how to find the Horcruxes, and they make a plan to go hunting for them that summer, only to have their plans derailed when Riddle manages to kidnap Snape to lure her to the department of mysteries to retrieve the prophecy for him.
Harriett is older than Harry by a year, but thanks to the Potter luck, both her and Harry sort of end up the same age, and both register as adopted by Snape, much to his annoyance.
Harriett's Snape was murdered in front of her before she was chucked into the veil, so when she sees this versions Voldemort in the atrium, she goes feral. Dumbledore arrives to the sight of two Harry Potter's completely obliterating Riddle, who barely manages to escape with his life, though not all his limbs, after Fudge and a bunch of Ministry employees see him.
Harriett launching herself at this worlds Snape, crying and calling him Daddy. Snape's soul leaves his body, as one of his worst nightmares is realized.
Harry's protest of absolutely fucking not!
Dumbledore twinkling.
Sirius (who survived) just as shocked as Snape and as outraged as Harry.
Minerva, confused, but gratified (I knew he had a heart in the somewhere.)
They play it off as the two of them being twins, and Harriet having been raised in secret, sent off to live elsewhere for her own safety.
Harriett going off on Dumbledore about trying to send the two of them to the Dursleys. Harriett showing him proof that the blood wards do not work the way he thinks they do, Dumbledore still arguing, and Harriet threatening to murder the Dursleys if he tries to force either her or Harry to live with them (it's far less than what those monsters deserve, for the way they treated us growing up. I was fortunate to escape, though barely with my life, I can only imagine how much worse they got for Harry, who did not escape them.)
Harry reluctantly admitting they were extremely abusive, showing off some of his scars, more numerous than Harriett's, and not as healed as hers, since her Snape helped her after he took her in.
Because of the modified adoption ritual they had used, and Harriett's Snape being chucked through the veil right after she was, just barely alive, the more this version of Snape interacts with Harriett, the more he starts to "remember" his alternate selfs life.
When Harriett came out of the veil, it exploded in a bright flash of multicolored lights, so no one actually saw her coming out, her appearance at the ministry was explained through "accidental magic, and magical twins bond" somehow summoning her to Harry.
Harriett's horcrux is all weird now, because the chunk belongs to a different Tom Riddle. She doesn't get visions like Harry, but she can still feel when the bastard is near.
They spend that summer in Grimauld Place with Sirius, the Weasley's and Snape, who is remembering more and more of his other life every day, and had started acting strange.
Sirius tries to treat Harriett like he does Harry, but it backfires cause she is not his biggest fan thanks to how he treats Snape. She'd never got on with her own Sirius either, and hadn't had much of a relationship with the man after he'd been exonerated and sent off to a private magical sanitarium in Belgium to heal up from his time in Azkaban.
Snapes Mark fades completely away about half way through the summer when his two selves have completely merged. He'd not been called once since the events at the Ministry, though they can't be certain he wasn't actually called and his mark was already too corrupted to register the summons.