(accidentally gains a new headcanon)
SO. I was complaining about how little screentime Remus Lupin gets in OotP and HBP, even though he should totally be writing back and forth with Harry the whole time (imagine OotP reasonable parent!Remus though: “Yes, I know Molly is a little over protective, it’s just because she loves you. Don’t listen to Sirius either, though, because he’s a bit reckless. Find the balance, it’ll be okay.”)
This thought spawned the idea of Hermione being in contact with Remus. Starting in November of ‘94 (“Harry got chosen for the Tournament and now he and Ron aren’t speaking and I’m so worried. I’m sorry, I didn’t know who else to go to.”), and carrying on through the end of sixth year, at which point everything changes. But it’s a combination of “I need a reasonable magical adult to talk to who isn’t actively teaching at the school” and “good gods why is nobody telling Remus things he deserves to be in the loop” and then they end up having a very close relationship and then someday she is the reasonable parental figure to the next generation in turn.