Even more; still more; indicating an increase in degree or intensity compared with what was just mentioned.
練習を続けた結果、彼の演奏はなお一層洗練されてきた。
As a result of continuing practice, his performance has become even more polished.
問題が深刻になったため、対応をなお一層強化する必要がある。
Because the problem has become serious, it's necessary to strengthen the response even more.
新しいデータにより、この理論の重要性がなお一層明らかになった。
New data has made the importance of this theory even clearer.