The Olden Trio
None of the students would expect it, but the teachers know otherwise. Albus, Minerva and Severus have drifted together over their years as members of staff at Hogwarts School of Witchcraft and Wizardry. Albus is the quirk, Severus is the snark, and Minerva is the passion.
The three work perfectly together and fit like pieces of a puzzle. Perhaps that is why they seem to get along well enough. Every new idea Albus comes up with is met with blunt critique from Severus and harsh criticism from Minerva. Albus appreciates that they don't immediately go along with his ideas like others would, such as Pomona Sprout or Rubeus Hagrid, and holds them dear to him because of this. He finds Minerva's nervousness and uncertainty amusing, and Severus's analysis to be insightful and that they often shed new light on things.
Though Minerva is Head of Gryffindor and Severus is the Head of Slytherin, the two aren't completely mortal enemies. They fight over the Quidditch Cup and taunt each other at matches, but they both know that it's all in good fun; one year when Slytherin takes the cup again, Severus gives Minerva the faintest of smiles and winks at her before discreetly toasting her at dinner the night of the final feast, and she blushes at the kind gesture and nods curtly at him, though she can't help but to smile slightly back. Albus sees the exchange and is overjoyed to the point that he thinks his swelling heart might burst.
When Albus is killed, Minerva stops speaking to Severus unless it's absolutely necessary, and even then she speaks with cold aloofness that would have shocked him if he hadn't known her better. Severus doesn't try to explain it to her; he knows that she would simply not believe it. During the Battle of Hogwarts, when Severus flees, he flees praying that Minerva will find out the truth—surely Potter would tell her everything when this whole thing was over with, should he not make it out of this ordeal alive.
After the Battle, Harry sits Minerva down and tells her everything that he feels he can about Albus and Severus's agreement, and how Severus died. Minerva collapses, sobbing, mourning over the losses of her two best friends.
When she becomes Headmistress, she spends much of her time speaking to their portraits. When she does, she feels that she somewhat has her friends back, though Albus warns her not to think so; it's not wise to get so attached to old portraits of lost loved ones.
She doesn't care—as long as she can speak with them one last time…
Author's Note: This one was a bit different than the Golden Trio because we already know what happens in Harry, Ron and Hermione's friendship, but we never really see the inner workings of other friendships. This Trio is not cannon, because it's not stated in the novels that Dumbledore, Snape and McGonagall are friends. This is only how I picture it. Hope you enjoyed. :)
Dumbly, Sev and Minnie © Jo Rowling