  We investigate the possibility and consequences of phase transitions from an
equation of state (EOS) describing nucleons and hyperons interacting via mean
fields of sigma, omega, and rho mesons in the recently improved quark-meson
coupling (QMC) model to an EOS describing a Fermi gas of quarks in an MIT bag.
The transition to a mixed phase of baryons and deconfined quarks, and
subsequently to a pure deconfined quark phase, is described using the method of
Glendenning. The overall EOS for the three phases is calculated for various
scenarios and used to calculate stellar solutions using the
Tolman-Oppenheimer-Volkoff equations. The results are compared with recent
experimental data, and the validity of each case is discussed with consequences
for determining the species content of the interior of neutron stars.
