I initially saw my t once a week and after a few weeks I told her that I feel I need to see her at least twice a week, but that I could not afford it financially, and would she be able to lower the fee so I could see her twice. She so generously reduced her fee to a ridiculous amount but I venture to say she would not have done it had she not felt I needed the twice weekly.
At the time I was a 'borderline' case. After three years of twice-weekly sessions she said she could no longer afford to see me at the very low fee, and since I was not able to pay full price, I just continued to see her once a week. It worked out just fine. I learned to make full use of the once-weekly session. She did allow for between-session calls.
After five satisfying years, I terminated treatment with her, (long story). I am a recovered borderline, hurray. Still have some issues I want to work through, have begun seeing a new t, and I did ask to see her twice a week. I told her that once I internalized a positive transference of her I would be able to manage with once a week.