This video explains how to properly blend normal maps It can also be used to add more intensity to normal maps if you duplicate your original normal map instead of adding a new one. Summary of the video: Add the Other normal map (that "other" could be a duplicate of the normal map you want to strengthen). Duplicate Other. Fill the blue channel of original Other with a 128 gray and set it to Overlay. Fill red and green channels of duplicate Other with white and set it to Multiply. Profit.
Things I learn as I make mods for Skyrim SE (I'm the dummy)