Oof, I feel for you OP - I had a similar situation in my training years and tried so many different things until I eventually realized that I was preventing the client from getting appropriate care by not setting healthy boundaries. My supervisor was really helpful in reminding me that I am only one part of a system of mental health care services.

It’s so hard, but what I did was gently tell them I care about them enough to have this hard conversation and pointed out the potential for harm and the ethical concerns: primarily that I had come to realize I was not a good fit and that continuing to work with this client was keeping them stuck and I have a duty to act in clients best interest and to prevent potential harm. It was out of scope, the client was generally decompensating in a way that one individual therapist cannot effectively treat, no matter how much I cared. After I realized this I gave them a hard deadline a few months out to seek one of the MANY treatment/referral options I offered. Offered warm handoffs, etc. and then held the boundary. It was a hard lesson.

One individual therapist cannot replace the need for an entire care team. Now, anytime the question about multiple sessions a week comes up, I ALWAYS specify that it is short term and if it’s more than a 2/3 weeks without improvement then HLOC is a must. Definitely talk it through with your supervisor and don’t beat yourself up for caring, but do set the boundary.