First, do you know the difference between deep tissue and deep pressure? In deep tissue, the massage therapist pushes, even tears through the top muscle layer to access the underlying layer and to rearrange (again tearing) muscle fibers that have scarred or formed adhesions to allow them to heal correctly. Not comfortable to have, and not comfortable the next day. This is an advanced technique that relatively few massage therapists learn.
In deep pressure, the massage therapist works the top layer of muscles with a lot of pressure, lifting the muscles group away from the bone and kneading it. It feels great, both during and after.
For deep pressure, telephone any massage studio and ask when you make your appointment for the massage therapist on the staff with the strongest pressure. For deep tissue, do a web search for "medical massage" in your local area.