  Using the idea of a smooth crossover from the hadronic matter with hyperons
to quark matter with strangeness, we show that the maximum mass of neutron
stars with quark matter core can be larger than those without quark matter
core. This is in contrast to the conventional softening of equation of state
due to exotic components at high density. Essential conditions to reach our
conclusion are (i) the crossover takes place at relatively low densities,
around 3 times the normal nuclear density, and (ii) the quark matter is
strongly interacting in the crossover region. By these, the pressure of the
system can be greater than that of purely hadronic matter in the crossover
region and leads to the maximum mass greater than 2 solar mass. This conclusion
is insensitive to the different choice of the hadronic equation of state with
hyperons. Several implications of this result to the nuclear incompressibility,
the hyperon mixing, and the neutrino cooling are also remarked.
