  We have constructed models of uniformly rotating compact stars including
hyperons, Bose-Einstein condensates of antikaons and quarks. First order phase
transitions from hadronic to antikaon condensed matter and then to quark matter
are considered here. For the equation of state undergoing phase transitions to
antikaon condensates, the third family of compact stars are found to exist in
the fixed angular velocity sequences. However, the third family solution
disappears when the compact stars rotate very fast. For this equation of state,
the fixed baryon number supramassive sequence shows a second stable part after
the unstable region but no back bending phenomenon. On the other hand, we
observe that the rotation gives rise to a second maximum beyond the neutron
star maximum for the equation of state involving phase transitions to both
antikaon condensed and quark matter. In this case, the back bending phenomenon
has been observed in the supramassive sequence as a consequence of the first
order phase transition from $K^-$ condensed to quark matter. And the back
bending segment contains stable configurations of neutron stars.
