Self-controlling dominance area of solutions (S-CDAS) reclassifies solutions in each front obtained by non-domination sorting to realize fine-grained ranking of solutions and improve the search performance of multi-objective evolutionary algorithms (MOEAs) in many-objective optimization problems (MaOPs). In this work, we further improve search performance of S-CDAS in MaOPs by analyzing genetic diversity in many-objective problems and enhancing crossover operators. First, we analyze genetic diversity in the population and the contribution of the conventional genetic operators when we increase the number of objectives, showing that the genetic diversity in the population significantly increases and offspring created by conventional crossover come to be not selected as parents because the operator becomes too disruptive and its effectiveness decrease. To overcome this problem, we implement crossover controlling the number of crossed genes (CCG) in S-CDAS and verify its effectiveness. Through performance verification using many-objective knapsack problems with 4-10 objectives, we show that the search performance of S-CDAS noticeably improves when we restrict the number of crossed genes. Also, we show that the effectiveness of CCG operator becomes significant as we increase the number of objectives. Furthermore, we show that offspring created by CCG are selected as parents more often than conventional crossover.