A rotor assembly is provided for a gas turbine engine. This rotor assembly includes a first rotor disk, a second rotor disk and a plurality of rotor blades. The first rotor disk is configured to rotate about a rotational axis. The second rotor disk is configured to rotate about the rotational axis. The rotor blades are arranged circumferentially around the rotational axis. Each of the rotor blades is mounted to the first rotor disk and to the second rotor disk. The rotor blades include a first rotor blade. The first rotor blade includes an attachment projecting axially along the rotational axis into a first pocket in the first rotor disk and a second pocket in the second rotor disk. The attachment has a dovetail cross-sectional geometry when viewed in a plane perpendicular to the rotational axis. A portion of the first rotor disk extends circumferentially across and covers the attachment.