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Frustrated magnets with a strong spin-lattice coupling can show rich magnetic phases and the associated fascinating phenomena. A promising platform is the breathing pyrochlore magnet CuInCr_{4}S_{8} with localized S=3/2Cr^{3+} ions, which is proposed to be effectively viewed as an S=6 Heisenberg antiferromagnet on the face-centered-cubic lattice. Here we unveil that CuInCr_{4}S_{8} exhibits a complex magnetic phase diagram with a small phase pocket (A phase) by means of magnetization, magnetostriction, magnetocapacitance, and magnetocaloric-effect measurements in pulsed high magnetic fields of up to 60 T. Remarkably, the appearance of A phase is accompanied by anomalous magnetostrictive and magnetocapacitive responses, suggesting the emergence of helimagnetism in contrast to the neighboring commensurate magnetic phases. Besides, the high-entropy nature is confirmed in the high-temperature side of A phase. These features are potentially related to a thermal fluctuation-driven multiple-q state caused by the magnetic frustration, which has been theoretically predicted but yet experimentally undiscovered in insulating magnets.