An offshore well-processing system includes a mobile offshore drilling unit and a remote well-processing device configured to be positioned on an offshore platform different from the mobile offshore drilling unit, the mobile offshore drilling unit defining at least one well center and comprising at least one primary drill rig including at least one drill floor and at least one hoisting system for raising and lowering tubular equipment through the at least one well center from/into a well in the seafloor. The mobile offshore drilling unit and the remote well-processing device are configured to be operationally coupled to each other; and the mobile offshore drilling unit is configured to assist in performing concurrent well-processing tasks on respective wells, including the first well processing task performed by the remote well-processing device on a first well and a second well-processing task concurrently performed by the offshore well-processing system on a second well.