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We demonstrate that ultra-high-energy collisions of particles falling freely from rest at infinity can occur in the field of near-extreme Kehagias-Sfetsos naked singularities related to the Horava gravity. However, the efficiency of escaping of created ultrarelativistic particles and the energy efficiency of the collisional process relative to distant observers are significantly lowered due to large gravitational redshift, which is substantially lower in comparison to those related to the collisions occurring close to the equatorial plane of near-extreme Kerr naked-singularity spacetimes. In the Kehagias-Sfetsos naked-singularity spacetimes, the energy efficiency relative to distant observers corresponds to the covariant energy of the colliding particles only. Finally, we demonstrate how the ultra-high-energy collisions are modified for charged particles if the Kehagias-Sfetsos naked singularities are immersed in a uniform magnetic field.