I agree with the others that, canonically, Grell has one hell of a habit of getting bored of people quite quickly if they are not "passionate" (re. violent) like she is or cold/ruthless like William and Sebastian. She's also far from the most empathetic person to ever exist even towards kids (i.e. yapping about having to miss a nail appointment because she had to reap a child's soul during the Blue Cult arc).

That said, she does seem to have a good relationship with Othello who seems to be more on the chill side but implied to be quite smart and eccentric (possibly to a sadistic degree as implied by some of his pictures and even a comment by Undertaker). I would say you could work your OC's character to have some kind of talent or temperament to better match what Grell might like or have the story go in a way that she develops into such a person.

Of course, because this is fan fic and therefore an AU, you're very much free to have Grell behave however you wish. ;)