In situ high-pressure x-ray diffraction, low-temperature resistivity, and magnetization experiments were performed on a La ₃₂ Ce ₃₂ Al ₁₆ Ni ₅ Cu ₁₅ bulk metallic glass (BMG). A sudden change in compressibility at ≈14 GPa and a rapid increase of resistivity at ≈12 K were detected, whereas magnetic phase transformation and magnetic field dependence of the low-temperature resistivity do not occur at temperatures down to 4.2 K. An interaction between conduction electrons and the two-level systems is suggested to explain the temperature and field dependences of resistivity of the BMG alloy. Although the cause of the unusual change in compressibility at ≈14 GPa is not clear, we believe that it could be linked with the unique electron structure of cerium in the amorphous matrix. An electronic phase transition in BMG alloys, most likely a second-order amorphous-to-amorphous phase transition, is suggested.