Magnetic skyrmions are vortex-like topological spin textures often observed to form a triangular-lattice skyrmion crystal in structurally chiral magnets with the Dzyaloshinskii-Moriya interaction. Recently, β-Mn structure–type Co-Zn-Mn alloys were identified as a new class of chiral magnet to host such skyrmion crystal phases, while β-Mn itself is known as hosting an elemental geometrically frustrated spin liquid. We report the intermediate composition system Co₇Zn₇Mn₆ to be a unique host of two disconnected, thermal-equilibrium topological skyrmion phases; one is a conventional skyrmion crystal phase stabilized by thermal fluctuations and restricted to exist just below the magnetic transition temperature T_c, and the other is a novel three-dimensionally disordered skyrmion phase that is stable well below T_c. The stability of this new disordered skyrmion phase is due to a cooperative interplay between the chiral magnetism with the Dzyaloshinskii-Moriya interaction and the frustrated magnetism inherent to β-Mn.