Do movement plans, like representations in working memory, share a limited pool of resources? If so, the precision with which each individual movement plan is specified should decrease as the total number of movement plans increases. To explore this, human participants made speeded reaching movements toward visual targets. We examined if preparing one movement resulted in less variability than preparing two movements. The number of planned movements was manipulated in a delayed response cueing procedure that limited planning to a single target (experiment 1) or hand (experiment 2) or required planning of movements toward two targets (or with two hands). For both experiments, initial movement direction variability was higher in the two-plan condition than in the one-plan condition, demonstrating a cost associated with planning multiple movements, consistent with the limited resource hypothesis. In experiment 3, we showed that the advantage in initial variability of preparing a single movement was present only when the trajectory could be fully specified. This indicates that the difference in variability between one and two plans reflects the specification of full motor plans, not a general preparedness to move. The precision cost related to concurrent plans represents a novel constraint on motor preparation, indicating that multiple movements cannot be planned independently, even if they involve different limbs.