We have performed in situ x-ray and neutron-diffraction measurements, and molecular dynamics simulations, of GeO2, an archetypal network-forming glass under pressure. Below 5 GPa, additional atoms encroaching on the first tetrahedral shell are seen to be a precursor of local coordination change. Between 6 and 10 GPa, we observe structures with a constant average coordination of approximately 5, indicating a new metastable, intermediate form of the glass. At 15 GPa, the structure of a fully octahedral glass has been measured. This structure is not retained upon decompression and, therefore, must be studied in situ.