If that is what you are looking for, I think the theoretical orientation of the T can make a big difference as to whether they might offer that. Ts who come from the humanist tradition and human potential movement might be a good starting point in locating a T who would provide this. I think some orientations of Ts are set up to provide short term therapy with a definite goal and they don't like to stray too far from that, so when the goal is reached, they are done. If you read descriptions of Ts before you choose, the humanist ones would use words like growth, journey, discovery, potential, healing, exploration, transformation, etc. Other styles of therapists can also provide longer term therapy, but choosing the humanist type might increase your odds of finding this.

When I first went to see my T, he said he doesn't do long term therapy, which he defined as longer than 3 years. However, we are now at the 6 year mark and he has never mentioned that 3 year thing since our first meeting. So I lucked out and found someone willing to keep going as long as I am benefiting. (I don't go every week, though.)