Two different variations of joint task switching led to different conclusions as to whether co-acting individuals share the same task-sets. The present study aimed at bridging this gap by replicating the version in which two actors performed two different tasks. Experiment 1 showed switch costs across two actors in a joint condition, which agreed with previous studies, but also yielded even larger switch costs in a solo condition, which contradicted the claim that actors represent an alternative task as their own when it is carried out by the co-actor but not when no one carries it out. Experiments 2 and 3 further examined switch costs in the solo condition with the aim to rule out possible influences of task instructions for and experiences with the other task that was not assigned to the actor. Before participants were instructed on the second of the two tasks, switch costs were still obtained without a co-actor when explicit task names (“COLOUR” and “SHAPE”) served as go/nogo signals (Experiment 2), but not when arbitrary symbols (“XXXX” and “++++”) served as go/nogo signals (Experiment 3). The results thus imply that switch costs depend on participants’ knowledge of task cues being assigned to two different tasks, but not on whether the other task is performed by a co-actor. These findings undermine the assumption that switch costs in the joint conditions reflect shared task-sets between co-actors in this procedure.