A combine harvester including a frame and two axial-flow crop processing rotors mounted to the frame. An inner support structure is located between the two rotors and mounted to the frame by a first linkage. Two outer support structures are located outboard of the two rotors and mounted to the frame by respective second and third linkages. The inner support structure and two outer support structures carry first and second pluralities of concave grate segments at a radial distance from the respective rotors. A concave adjustment system includes a first actuator coupled to the first linkage which is configured to raise and lower the inner support structure. A second actuator is coupled to the second and third linkages and is configured to raise and lower the two outer support structures. The first linkage includes a first rockshaft mounted to the frame and aligned perpendicular to the rotation axis. The second and third linkages include and share a second rockshaft that is arranged coaxial to the first rockshaft.