  Using 567 $pb^{-1}$ of data collected with the BESIII detector at a
center-of-mass energy of $\sqrt{s}=$ 4.599 $GeV$, near the
$\Lambda_{c}^{+}\Lambda_{c}^{-}$ threshold, we study the singly
Cabibbo-suppressed decays $\Lambda_c^{+}\to p\pi^{+}\pi^{-}$ and
$\Lambda_c^{+}\to pK^{+}K^{-}$. By normalizing with respect to the
Cabibbo-favored decay $\Lambda_c^{+}\to pK^{-}\pi^{+}$, we obtain ratios of
branching fractions: $\frac{\mathcal{B}(\Lambda_c^{+}\to
p\pi^{+}\pi^{-})}{\mathcal{B}(\Lambda_c^{+}\to pK^{-}\pi^{+})}$ = $(6.70 \pm
0.48 \pm 0.25)\%$, $\frac{\mathcal{B}(\Lambda_c^{+}\to
p\phi)}{\mathcal{B}(\Lambda_c^{+}\to pK^{-}\pi^{+})}$ = $(1.81 \pm 0.33 \pm
0.13)\%$, and $\frac{\mathcal{B}(\Lambda_c^{+}\to
pK^{+}K^{-}_{\text{non-}\phi})}{\mathcal{B}(\Lambda_c^{+}\to pK^{-}\pi^{+})}$ =
$(9.36 \pm 2.22 \pm 0.71)\times10^{-3}$, where the uncertainties are
statistical and systematic, respectively. The absolute branching fractions are
also presented. Among these measurements, the decay $\Lambda_c^{+}\to
p\pi^{+}\pi^{-}$ is observed for the first time, and the precision of the
branching fraction for $\Lambda_c^{+}\to pK^{+}K^{-}_{\text{non-}\phi}$ and
$\Lambda_c^{+}\to p\phi$ is significantly improved.
