The HyperCP experiment (Fermilab E871) has the largest recorded sample
of $\Omega^-$ hyperon decays, allowing us to search for three rare decay
modes, each with five charged tracks in the final state. We present new
measurements of: 1) $\Omega^-\to\Xi^-\pi^+\pi^-$; 2) $\Omega^- \to
\Xi^{0*}(1530)\pi^-$; and 3) the flavor-changing-neutral-current decay
$\Omega^- \to \Xi^-\mu^+\mu^-$. We normalize these measurements to the
decay $\Omega^- \to \Lambda K^-$ in both the five-track topology
$\Lambda \to p \pi^-$, $K^- \to \pi^- \pi^- \pi^+$, and the three-track
topology where the $K^-$ does not decay in the spectrometer.