There should be sheathing under most of the siding and plywood in the corners. (If it's like my builder) I did what you are suggesting and had a pro, (using the term loosely) do the job of adding additional board insulation to the house and then siding.
The main problem is that he had trouble fastening the siding to the new double layer of insulation and sheathing. I didn't find out until a few years later when the siding started blowing off.
I think the proper way would be to replace the sheathing with the insulation board.