Disclaimer: I do not own Harry Potter. I'm pretty sure my imagination is my own, though. Unless it's not . . . whoa. Spooky idea.
In an alternate universe, Draco Malfoy failed to sneer or insult someone for two or three whole days at a time and hovered over Neville Longbottom like an overprotective older brother.
Remus Lupin turned into a werebunny every fullmoon.
Sirius "Lord Black" Black lived under Moony's bed and collected mothballs.
Lucius Malfoy and Severus Snape were pen-pals, and giggled over a child Harry Potter, who was often seen in their company with a disposition similar to Grumpy Cat's and the face to match, irate from having his hair braided and his nails polished.
Lily Potter nee Evans ruled over the world with a sunny smile and a steely glint in her eyes.
James Potter ran a bar called the Sotted Potter that only sold non-alcoholic drinks. Favorites were the lemonade, the chocolate milk and the weaseljuice in a glass (given only to particularly annoying customers).
Tom Riddle (aka Voldemort) cowered at Lord Lily's feet and almost cried whenever she cheerfully called him Tim.
Barty Crouch Jr. had an extraordinary brain and owned a pocket watch that whispered things to him when he touched it.
Dolores Umbridge ran a little group called TAA (Torture Addicts Anonymous) and was checked on daily by her parole officer, Molly Weasely.
Narcissa Malfoy randomly adopted people and brought them home. Horace Slughorn told her that maybe she should join AAA (Adopting Addicts Anonymous). He never joked about it again.
Peter Pettigrew owned a coffee shop called Scabber's. Despite the name, it was a very pleasant place where ladies liked to flock and gossip. Sometimes he liked to join them.
Bellatrix LeStrange nee Black taught knitting and owned a large clothing franchise and also a night club where she sometimes liked to go and dance as a stripper.
Albus Dumbledore worked not only as Headmaster of Hogwarts School for the Magically Inclined but also doubled as a secret agent spy called Gandalf the Gray.
Minerva McGonagall starred as the starry-eyed, helpless, wrist-wringing heroine in one of Lockhart's stories. She was not amused. Lockhart grew to be in awe of and fear her unamusement.
Finch was in a wild, passionate love affair with a water nymph who lived in the Hogwarts lake who took one look at him and fell in perpetual lust. He didn't complain.
Mrs. Norris divorced Mr. Norris to live with the Sorting Hat and occasionally alarm him by using him as a scratching post.
The Basilisk fell into a mutually-beneficent rivalry with Aragog, and they liked to scare people who wandered into the Forbidden Forest. Aragog had a cousin who lived in a place called Cirith Ungol. Apparently, a very out-of-the-way place. Shelob liked oatmeal and little creatures called hobbits, or something.
Madam Pomfrey ruled over her hospital wing with an iron fist and a steel bedside manner.
Voldemort got letters once a month from an admirer. Saruman, or something like that.
Harry Potter's reputation as The-Boy-Who-Just-Kept-Living was cemented when he got a nasty paper cut and survived it.
Merlin had no beard.