Virtually all intercalation compounds exhibit significant changes in unit cell volume as the working ion concentration varies. Na_xFePO₄ (0 < x < 1, NFP) olivine, of interest as a cathode for sodium-ion batteries, is a model for topotactic, high-strain systems as it exhibits one of the largest discontinuous volume changes (∼17% by volume) during its first-order transition between two otherwise isostructural phases. Using synchrotron radiation powder X-ray diffraction (PXD) and pair distribution function (PDF) analysis, we discover a new strain-accommodation mechanism wherein a third, amorphous phase forms to buffer the large lattice mismatch between primary phases. The amorphous phase has short-range order over ∼1nm domains that is characterized by a and b parameters matching one crystalline end-member phase and a c parameter matching the other, but is not detectable by powder diffraction alone. We suggest that this strain-accommodation mechanism may generally apply to systems with large transformation strains.