  We report measurements of Shubnikov-de Haas oscillations in the giant Rashba
semiconductor BiTeI under applied pressures up to $\sim 2\,\mathrm{GPa}$. We
observe one high frequency oscillation at all pressures and one low frequency
oscillation that emerges between $\sim 0.3-0.7\,\mathrm{GPa}$ indicating the
appearance of a second small Fermi surface. BiTeI has a conduction band bottom
that is split into two sub-bands due to the strong Rashba coupling, resulting
in a `Dirac point'. Our results suggest that the chemical potential starts
below the Dirac point in the conduction band at ambient pressure and moves
upward, crossing it as pressure is increased. The presence of the chemical
potential above this Dirac point results in two Fermi surfaces. We present a
simple model that captures this effect and can be used to understand the
pressure dependence of our sample parameters. These extracted parameters are in
quantitative agreement with first-principles calculations and other
experiments. The parameters extracted via our model support the notion that
pressure brings the system closer to the predicted topological quantum phase
transition.
