I had decided to re-face my existing stairs with engineered oak treads. I completed the set of stairs leading to the lower level without problem by cutting the nosing off the existing "ruff" treads and installing new risers and the oak treads over the existing ones. The bottom stair set is completely enclosed.
Then the problem was realized.
My home is a spit entry and the set of stairs leading to the main level has 6 treads with the first 3 exposed on the right side. If I use the same method as the bottom set you will be able to see the old tread and riser from the side view.
To use the engineered treads over existing treads, cut the return noising off the existing tread, (most times the return nosing is nailed and glued on and can be removed easily) take the Scotia mold off the front and side under the treads.
Install the stair brackets to hide the part you cut off and replace the Scotia mold front and over the brackets.
Here is a link to show you some brackets.