When someone grants you modify rights, that should extend to anything they own, including prim parts on the avatar they are wearing. Maybe not being able to toss them into Appearance mode and adjust the sliders, but at least to be able to modify prim parts.
Last night, I was trying to assist my mate in making some fairly simple (for me) modifications to her avatar. She's wearing a +copy/+mod/NO Trans furry avatar from Luskwood, with prim hair. I own the same avatar, in the male version, and I had no trouble editing my prim hair to change the color and re-style it a bit. I wanted to do the same for her, as she wants a white stripe in her hair, and there's one prim under the top layer of her hair that is completely the wrong color.
She granted me modify rights for her stuff, but I can't modify her hair or her fox-head prims while she is wearing them. I have no trouble doing it myself on my own avatar while I am wearing it.
I tried to talk her through it, and she wound up messing up the avatar so badly that she had to rez a fresh copy and start over. She just doesn't have the knack for building and modifying things in SL, even with someone giving her concise, step-by-step instructions.
I don't want to ask her for her password, so I can log on as her and do it for her. And we live in different states, so I can't have her log in, and then do it at her end on her computer. This should be as simple as editing the color of her prim purse. Can we have that, please?