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