  The cross section of the process $e^+e^- \to K_S^0
K^{\pm}\pi^{\mp}\pi^+\pi^-$ has been measured for the first time using a data
sample of 185.4 pb$^{-1}$ collected with the CMD-3 detector at the VEPP-2000
$e^+e^-$ collider. With the $K_S^0\to\pi^+\pi^-$ decay detection, 373$\pm$20
and 514$\pm$28 signal events have been selected with six and five reconstructed
tracks, respectively, in the center-of-mass energy range 1.6--2.0 GeV. The
total systematic uncertainty of the cross section is about 15\%. The study of
the production dynamics allows us to extract contribution from the $e^+e^- \to
f_1(1285)\pi^+\pi^-$ intermediate state and to measure the corresponding cross
section. The intermediate states with the $f_1(1420)$ and $f_1(1510)$
resonances have been observed.
