A multi-ply seal ring includes an inner seal ring and an outer seal ring. The inner seal ring includes a plurality of discrete inner ring segments disposed circumferentially about an axis in an annular array. The inner ring segments are arranged end-to-end within the annular array. The inner seal ring is engaged with and nested within the outer seal ring. In addition or alternatively, the outer seal ring may include a plurality of discrete outer ring segments disposed circumferentially about the axis in an annular array.