Phase transformations in metallic grain boundaries (GBs) present significant fundamental interest in the context of thermodynamics of low-dimensional physical systems. We report on atomistic computer simulations of the Cu-Ag system that provide direct evidence that GB phase transformations in a single-component GB can continue to exist in a binary alloy. This gives rise to segregation-induced phase transformations with varying chemical composition at a fixed temperature. Furthermore, for such transformations we propose an approach to calculations of free energy differences between different GB phases by thermodynamic integration along a segregation isotherm. This opens the possibility of developing quantitative thermodynamics of GB phases, their transformations to each other, and critical phenomena in the future. ; Comment: 11 pages, 4 figures in Phys Rev B Rapid Communication 2015