  The decay $D^{+} \rightarrow K_{S}^{0} \pi^{+} \pi^{+} \pi^{-}$ is studied
with an amplitude analysis using a data set of 2.93${\mbox{\,fb}^{-1}}$ of
$e^+e^+$ collisions at the $\psi(3770)$ peak accumulated by the BESIII
detector. Intermediate states and non-resonant components, and their relative
fractions and phases have been determined. The significant amplitudes, which
contribute to the model that best fits the data, are composed of five
quasi-two-body decays $ K_{S}^{0} a_{1}(1260)^{+}$, $ \bar{K}_{1}(1270)^{0}
\pi^{+}$ $ \bar{K}_{1}(1400)^{0} \pi^{+}$, $ \bar{K}_{1}(1650)^{0} \pi^{+}$,
and $ \bar{K}(1460)^{0} \pi^{+}$, a three-body decays
$K_{S}^{0}\pi^{+}\rho^{0}$, as well as a non-resonant component $
K_{S}^{0}\pi^{+}\pi^{+}\pi^{-}$. The dominant amplitude is $ K_{S}^{0}
a_{1}(1260)^{+}$, with a fit fraction of $(40.3\pm2.1\pm2.9)\%$, where the
first and second uncertainties are statistical and systematic, respectively.
