We investigated the role of task constraints on inter-personal interactions. Twenty-one pairs of co-workers performed a finger force production task on force sensors placed at two ends of a seesaw-like apparatus and matched a combined target force of 20N for 23 seconds over ten trials. There were two experimental conditions: 1) FIXED: the seesaw apparatus was mechanically held in place so that the only task constraint was to match the 20N resultant force, and 2) MOVING: the lever in the apparatus was allowed to rotate freely around its fulcrum, acting like a seesaw, so an additional task constraint to (implicitly) balance the resultant moment was added. We hypothesized that the additional task constraint of moment stabilization imposed on the MOVING condition would deteriorate task performance compared to the FIXED condition; however, this was rejected as the performance of the force matching task was similar between two conditions. We also hypothesized that the central nervous systems (CNSs) would employ distinct co-working strategies or inter-personal motor synergy (IPMS) between conditions to satisfy different task constraints, which was supported by our results. Negative covariance between co-worker's forces in the FIXED condition suggested a force stabilization strategy, while positive covariance in the MOVING condition suggested a moment stabilization strategy, implying that independent CNSs adopt distinct IPMSs depending on task constraints. We speculate that, in the absence of a central neural controller, shared visual and mechanical connections between co-workers may suffice to trigger modulations in the cerebellum of each CNS to satisfy competing task constraints.