“Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will spend its whole life believing it is stupid.” – Einstein
I believe I can help you with your question. Yes, you are able to talk with your therapist's supervisor, especially if that therapist is a student or works in a larger agency. May I ask what your concerns are about your therapist? Have you tried to talk to him/her directly about these concerns?
My T isn't a student, she is self employed and has several years experience and is well qualified.
I have attachment issues (I'm the son of a narcissistic mother and had no parental love or affection) and chose the T I did in order to create an 'attachment' for real, in a safe environment with a professional to help me understand the why's and hows and to learn how to deal with it an move on. I've taken the need for friendship from T to sessions and to some extent she has met those needs. Now she feels I see her to attempt to forge a personal relationship with her.
We have discussed this on a few occasions and she now feels my that my seeing her and my feelings for her are a hinderance to my progress.