Rate of decline of the production cross section of superheavy nuclei with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>Z</mml:mi><mml:mo>=</mml:mo><mml:mn>114</mml:mn><mml:mo>–</mml:mo><mml:mn>117</mml:mn></mml:mrow></mml:math> at high excitation energies

The production cross sections of superheavy nuclei with charge numbers $114-117$ are predicted in the $(5-9)n$-evaporation channels $^{48}$Ca-induced complete fusion reactions for future experiments. estimates synthesis capabilities based on a uniform and consistent set input nuclear data provided by multidimensional macroscopic-microscopic approach. contributions various factors to final section discussed. As shown, specific interplay between survival probabilities unexpectedly leads relatively slow decline total cross-sections increasing excitation energy. This effect is supported favorable arrangement fission barriers protecting compound nucleus against splitting concerning energetic thresholds emission successive neutrons. In particular, formation $5n$-, $6n$-, some cases even $7n$-evaporation still promising. may offer new opportunity unknown neutron-deficient isotopes.