Abstract: Possibility of kaon-condensed phase in hyperon-mixed matter is considered as high-density multi-strangeness system, which may be realized in neutron stars. The interaction model is based on chiral symmetry for kaon-baryon and kaon-kaon interactions, being combined with the relativistic mean-field theory for two-body baryon-baryon (B-B) interaction. In addition, the Lorentz invariant forms of many-baryon repulsive force (MBR) and three-nucleon attractive force (TNA) are phenomenologically introduced, where unknown parameters are fixed to satisfy the saturation properties of symmetric nuclear matter and the causality condition that the sound velocity should be less than the speed of light. It is shown that the equation of state with kaon condensation in hyperon-mixed matter is stiff enough to be consistent with recent observations of massive neutron stars.