An anomaly in differential scanning calorimetry has been reported in a number of metallic glass materials in which a broad exothermal peak was observed between the glass and crystallization temperatures. The mystery surrounding this calorimetric anomaly is epitomized by four decades long studies of Pd-Ni-P metallic glasses, arguably the best glass-forming alloys. Here we show, using a suite of in situ experimental techniques, that Pd-Ni-P alloys have a hidden amorphous phase in the supercooled liquid region. The anomalous exothermal peak is the consequence of a polyamorphous phase transition between two supercooled liquids, involving a change in the packing of atomic clusters over medium-range length scales as large as 18 Å. With further temperature increase, the alloy reenters the supercooled liquid phase, which forms the room-temperature glass phase on quenching. The outcome of this study raises a possibility to manipulate the structure and hence the stability of metallic glasses through heat treatment.