It is rare for me to get a request to re-patina a ring. I try to let them know up front it will wear away. I don’t charge people if they ask though.
I do it the same the second time,. I just don’t have to remove any fire scale.
Here are my steps when applying a new patina, or even reapplying. I use the Sally’s Beauty Supply Miracle buffing block with the white and grey side. I use the grey side to remove any fire scale on the ring and then buff with the white side. I’ll then clean the ring with acetone, apply the patina with black max. Once the ring is black, I will then buff the patina with the white side to a high black shine. This seem to “set” the patina a little more. I’ll then remove the patina from the high points of the detail with the grey side and finish with one last buff on the white side all over the ring.
Here is the link to the buffing block: