  We search for the semi-leptonic decays $\Lambda_c^+ \to \Lambda \pi^+ \pi^-
e^+ \nu_e$ and $\Lambda_c^+ \to p K_S^0 \pi^- e^+ \nu_e$ in a sample of 4.5
$\mathrm{fb}^{-1}$ of $e^{+}e^{-}$ annihilation data collected in the
center-of-mass energy region between 4.600 GeV and 4.699 GeV by the BESIII
detector at the BEPCII. No significant signals are observed, and the upper
limits on the decay branching fractions are set to be $\mathcal{B}(\Lambda_c^+
\to \Lambda \pi^+ \pi^- e^+ \nu_e)<3.9\times10^{-4}$ and
$\mathcal{B}(\Lambda_c^+ \to p K_S^0 \pi^- e^+ \nu_e)<3.3\times10^{-4}$ at the
90% confidence level, respectively.
