According to the decomposition thesis, perceptual experiences resolve without remainder into their different modality-specific components. Contrary to this view, I argue that certain cases of multisensory integration give rise to experiences representing features of a novel type. Through the coordinated use of bodily awareness—understood here as encompassing both proprioception and kinaesthesis—and the exteroceptive sensory modalities, one becomes perceptually responsive to spatial features whose instances couldn’t be represented by any of the contributing modalities functioning in isolation. I develop an argument for (...) this conclusion focusing on two cases: 3D shape perception in haptic touch and experiencing an object’s egocentric location in crossmodally accessible, environmental space. (shrink)