We utilize synchrotron X-ray diffraction measurements, conducted inside a diamond anvil cell, to analyze the high-pressure stability of Mg/Nb multilayered nanocomposites of equal (1:1) and unequal (1:10) thickness ratios. At larger layer thicknesses, Mg in these nanocomposites exists in its traditional hexagonal close packed (hcp) structure, while below a critical layer thickness of 7-8 nm, the Mg structure is found to transform into an interface strain-induced metastable pseudomorphic body center cubic (bcc) crystal structure. The hcp Mg present in the larger layer thicknesses exhibits an hcp-to-bcc phase transformation at pressures greater than 44 GPa, and this pressure value is found to vary between the equal and unequal Mg/Nb nanocomposite thickness ratios. On the other hand, the pseudomorphic bcc Mg structure is stable up to pressures of 60 GPa. Additionally, the compressibility of the pseudomorphic bcc Mg structure under pressure is shown to be fundamentally different from the bulk (nonlaminated) bcc Mg structure formed under high pressures. These results indicate that interface strain engineering, and an appropriate choice of the adjacent layer material, might be a viable pathway for tuning the structure and properties of the pseudomorphic bcc Mg structure.