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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 …