  The K$^-$ condensation and quark deconfinement phase transitions are
investigated in the modified quark-meson coupling model. It is shown that K$^-$
condensation is suppressed because of the quark deconfinement when
$B^{1/4}<$202.2MeV, where $B$ is the bag constant for unpaired quark matter.
With the equation of state (EOS) solved self-consistently, we discuss the
properties of compact stars. We find that the EOS of pure hadron matter with
condensed K$^-$ phase should be ruled out by the redshift for star EXO0748-676,
while EOS containing unpaired quark matter phase with $B^{1/4}$ being about
180MeV could be consistent with this observation and the best measured mass of
star PSR 1913+16. We then probe into the change of the phase structures in
possible compact stars with deconfinment phase as the central densities
increase. But if the recent inferred massive star among Terzan 5 with
M$>$1.68M$_{\odot}$ is confirmed, all the present EOSes with condensed phase
and deconfined phase would be ruled out and therefore these exotic phases are
unlikely to appear within neutron stars.
