As someone whose very first anime/anime crush was Inuyasha, I have a soft spot for white-haired animated men, and Qifrey is hitting all the right boxes for me, especially given his... range
here's an idea: yandere Qifrey who's just a liiiittle too fond of his new adult apprentice... just a little too eager to have the opportunity of teaching you magic as an excuse to spend time with you
"The best way to learn magic is to incorporate it into your everyday life!" says the man who uses this as a justification to GLUE himself to you to cater to his your every curiosity, to answer any possible question you may have about ANYTHING. He is constantly finding some sort of reason to be around you, always finding something new to teach you or talk to you about
It would be oh so convenient for him if you had a situation similar to Coco's where you're either an outsider or an unpracticed witch who, through an accident with magic or maybe even an encounter with a certain cult of Forbidden Magic users, has lost your home and needs a new place to stay, provided by none other than Qifrey himself. Why, after such a horrible ordeal, you'll especially need his company to help cheer you up and keep you in good spirits, won't you?
Any involvement with the Brimmed Caps is also more ammunition for him to justify his actions and behavior to anyone who may question his intentions. No no no, you see, he simply MUST be sure to maintain a constant vigil over you, because what if those evil witches were to return to target you? Isn't tracking them down and stopping them more important than some... 'perceived peculiarities in his behavior towards you'?
Of course, it would also be particularly sinister if this man who knows a thing or two about keeping secrets were to also have access to any sort of thing - say, perhaps a spell- that could do something crazy like, i dunno, alter your memories, maybe even erase them leaving you none the wiser?
An unfortunate discovery as you stumble upon certain 'art' of his involving you and particularly intimate areas of your body? Forgotten. You accidentally let out a shocked gasp while eavesdropping on a conversation where another person accuses your teacher of being a creep and you suddenly see some of his actions in a significantly less flattering light? No, that didn't happen. A confession of his undying devotion and love that ends with total rejection and a lost of trust? Consider that memory wiped clean for this selfish spellcaster to someday try again
Qifrey will bite his tongue and yearn for you in silence, wiping your mind as many times as it takes as long as it maintains your friendship. Whatever it takes to keep you close. Whatever it takes you keep you safe. Whatever it takes to keep you his.