You should not be able to adjust the strength of a normal map at all! The strength is permanently mapped into the map.* Any adjustment would therefore not reflect the original normal map. But yes you can increase the contrast of the map, or set teh range of the normal component BUT THATS NOT WHAT YOU WANT TO EVER DO, as it defeats the purpose of using normal maps!
IF you wanted the fidelty of a normal map generated then it makes no sense to alter it. If on the otherhand you DID want to alter it youd have used a bump map instead, as it produces better derivatives when scaled. (you can use the displacement part a s a bump map)
- see the map is directions, directions cant be scaled. This is kind of the IDEA behind why you'd use normal maps.
See trasfroming normals is something that does not elementary work consistently so one should be very cerefull with the math behind this. Basically wah one should do is integrate them back to bump and then re derivate them to normals.