I tried asking for an object once with my ex T. I had thought of asking her to choose one of my favourite marbles from a bag, and then "giving" me that because I knew she wouldn't give me any object of hers.

She said she had to seek peer consultation and supervision and they advised her not to in case it "promoted dependency". (I don't agree)

I've also asked my current T if I could have a photo of her for the same thing and she ignored my request every time I brought it up, so I assume it's a "no".

I really hope you get a better response should you feel a transitional object might help.