We have measured the branching fractions of the Cabibbo-suppressed decays $\Lambda^+_c$ $\to$ $\Lambda^{0}$ $K^+$ and $\Lambda^+_c$ $\to$ $\Sigma^0$ $K^+$
%(measured with improved accuracy).
relative to the Cabibbo-allowed decay modes $\Lambda^+_c$ $\to$ $\Lambda^{0}$ $\pi^+$ and $\Lambda^+_c$ $\to$ $\Sigma^0$ $\pi^+$ to be $ 0.044~ \pm ~0.004 ~(\textnormal{stat.})~ \pm ~0.002 ~(\textnormal{syst.})$ and $ 0.040~ \pm ~0.005 ~(\textnormal{stat.})~ \pm ~0.004
~(\textnormal{syst.})$, respectively.
We also present the first observation of $\Lambda^+_c$ $\to$ $\Lambda^{0}$ $K^+ \pi^+ \pi^-$ and have measured the branching fraction relative to $\Lambda^+_c$ $\to$ $\Lambda^{0}$ $\pi^+$ to be $0.266~ \pm ~0.027 ~(\textnormal{stat.})~ \pm ~0.032 ~(\textnormal{syst.})$. The
upper limit of the branching fraction into the decay $\Lambda^+_c$ $\to$ $\Sigma^0$ $K^+ \pi^+ \pi^-$ relative to  $\Lambda^+_c$ $\to$ $\Sigma^0$ $\pi^+$ has been measured to be
%7.6 \times ~10^{-4}$
$ < 3.9 \times ~10^{-2}$ at the 90\% confidence level. This analysis was performed using a data sample of
%approximately
 125 fb$^{-1}$ (integrated luminosity) collected by the \babar$\ $detector at the PEP-II asymmetric-energy $B$ Factory at the Stanford Linear Accelerator Center.
All results presented in this conference contribution are preliminary.