The invention relates to a wind turbine system comprising a support structure with a plurality of wind turbine modules mounted to the support structure. A control system is arranged to enter a service mode wherein service can be performed in the wind turbine system by applying a first control command to a first subset of wind turbine modules for terminating power production. A second control command is applied to a second subset of wind turbine modules for bringing the second subset of wind turbine modules into an damping mode where each of the wind turbine modules of the second subset is operated and/or positioned to damp vibrations, actively and/or passively, of at least one wind turbine module of the first subset of wind turbine modules.