The core of neutron-star matter is supposed to be at a much higher density than the normal nuclear-matter density, for which various possibilities have been suggested, such as, for example, meson or hyperon condensation and/or deconfined quark or color-superconducting matter. In this work, we explore the implication on hadron physics of a dense compact object that has three “phases”: nuclear matter at the outer layer, kaon condensed nuclear matter in the middle, and strange quark matter at the core. Using a drastically simplified but not unreasonable model, we develop the scenario where the different phases are smoothly connected with the kaon condensed matter playing a role of a “doorway” to a quark core, the equation of state of which with parameters restricted within the range allowed by nature could be made compatible with the mass vs radius constraint given by the 1.97-solar-mass object PSR J1614-2230 recently observed.