  CP violation is an excellent tool for probing flavor dynamics as we learnt
first with $K_L \to 2 \pi$ and later also with the weak decays of beauty
mesons. LHCb 2019 data have shown CP violation for the first time in $D^0\to
K^-K^+$ vs. $D^0\to\pi^-\pi^+$. Searching for CP asymmetries is of great
interest in charm quark sector in the Standard Model (SM) or even more beyond
it. In charm hadron decays, lots of work had focused on two-body final states,
and the measurements of CP asymmetries in three- or four-body final states are
rare. Dalitz plots have shown an excellent record for three-body final states,
and more results are desired for four-body ones. In this work we study CP
asymmetries in the decays $\Lambda^+_c \to p K^-\pi^+\pi^0$/$\Lambda
\pi^+\pi^+\pi^-$/$pK_S\pi^+\pi^-$, where the SM gives zero values for the first
two channels, while $3.3 \times 10^{-3}$ for the last one due to $K^0 - \bar
K^0$ oscillation. We performed a fast Monte Carlo simulation study by using
electron-positron annihilation data of 1~$\textrm{ab}^{-1}$ at center-of-mass
energy $\sqrt{s}\, =\, 4.64$ GeV. The data is expected to be available by the
next generation Super Tau Charm Facility proposed by China and Russia with one
year (or even less) data taking operation. The results indicate that a
sensitivity at the level of 0.2$\sim$0.5% is accessible for these processes,
which would be enough to measure nonzero CP-violating asymmetries as large as
1%.
