I've had ideas for favors that I've never asked for (though my desire for them isn't extremely strong and I suspect the favor may actually be harmful to me in the long-run). For instance, I've thought about asking T not to look at me, asking one of us to wear sunglasses, or asking T if we could talk with the lights off, which would make me feel more comfortable making eye contact. But mostly, I'd feel very strange for asking those things and T may think they are strange requests. So I've never seriously considered asking, especially because it would probably be such a fuss and make all parties feel awkward. I'm somewhat with you in fearing to ask for anything beyond normal protocol.

My T just recently moved to a new office though, and I really wished I could have a picture of her old office to remember it. I didn't have to ask though, because she suggested I take a picture when I talked about how I would miss the room. Maybe there is a way for you to subtly bring it up? I feared I would seem like a creep to ask for a pic, but she had no problem with it and even left the room to give me privacy. You never know for sure!