  We present a new analysis of previously published of SuperCDMS data using a
profile likelihood framework to search for sub-GeV dark matter (DM) particles
through two inelastic scattering channels: bremsstrahlung radiation and the
Migdal effect. By considering these possible inelastic scattering channels,
experimental sensitivity can be extended to DM masses that are undetectable
through the DM-nucleon elastic scattering channel, given the energy threshold
of current experiments. We exclude DM masses down to $220~\textrm{MeV}/c^2$ at
$2.7 \times 10^{-30}~\textrm{cm}^2$ via the bremsstrahlung channel. The Migdal
channel search provides overall considerably more stringent limits and excludes
DM masses down to $30~\textrm{MeV}/c^2$ at $5.0 \times 10^{-30}~\textrm{cm}^2$.
