Multisensory integration enables rapid and accurate behavior. To orient in space, sensory information registered initially in different reference frames has to be integrated with the current postural information to produce an appropriate motor response. In some postures, multisensory integration requires convergence of sensory evidence across hemispheres, which would presumably lessen or hinder integration. Here, we examined orienting gaze shifts in humans to visual, tactile, or visuotactile stimuli when the hands were either in a default uncrossed posture or a crossed posture requiring convergence across hemispheres. Surprisingly, we observed the greatest benefits of multisensory integration in the crossed posture, as indexed by reaction time (RT) decreases. Moreover, such shortening of RTs to multisensory stimuli did not come at the cost of increased error propensity. To explain these results, we propose that two accepted principles of multisensory integration, the spatial principle and inverse effectiveness, dynamically interact to aid the rapid and accurate resolution of complex sensorimotor transformations. First, early mutual inhibition of initial visual and tactile responses registered in different hemispheres reduces error propensity. Second, inverse effectiveness in the integration of the weakened visual response with the remapped tactile representation expedites the generation of the correct motor response. Our results imply that the concept of inverse effectiveness, which is usually associated with external stimulus properties, might extend to internal spatial representations that are more complex given certain body postures.