Using the idea of smooth crossover from hadronic matter with hyperons to quark matter with strangeness, we show that the maximum mass ( M max ) of neutron stars with quark matter cores can be larger than those without quark matter cores. This is in contrast to the conventional softening of the equation of state due to exotic components at high density. The essential conditions for reaching our conclusion are that (1) the crossover takes place at relatively low densities, around three times the normal nuclear density and (2) the quark matter is strongly interacting in the crossover region. From these, the pressure of the system can be greater than that of purely hadronic matter at a given baryon density in the crossover density region and leads to M max greater than 2 solar mass. This conclusion is insensitive to the different choice of the hadronic equation of state with hyperons. We remark upon several implications of this result to the nuclear incompressibility, the hyperon mixing, and the neutrino cooling.
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