It can be shown empirically and theoretically that inferences based on established metrics used to assess multisensory integration with BOLD fMRI data, such as superadditivity, are dependent on the particular experimental situation. For example, the law of inverse effectiveness shows that the likelihood of finding superadditivity in a known multisensory region increases with decreasing stimulus discriminability. In this paper, we suggest that Sternberg's additive-factors design allows for an unbiased assessment of multisensory integration. Through the manipulation of signal-to-noise ratio as an additive factor, we have identified networks of cortical regions that show properties of audio-visual or visuo-haptic neuronal convergence. These networks contained previously identified multisensory regions and also many new regions, for example, the caudate nucleus for audio-visual integration, and the fusiform gyrus for visuo-haptic integration. A comparison of integrative networks across audio-visual and visuo-haptic conditions showed very little overlap, suggesting that neural mechanisms of integration are unique to particular sensory pairings. Our results provide evidence for the utility of the additive-factors approach by demonstrating its effectiveness across modality (vision, audition, and haptics), stimulus type (speech and non-speech), experimental design (blocked and event-related), method of analysis (SPM and ROI), and experimenter-chosen baseline. The additive-factors approach provides a method for investigating multisensory interactions that goes beyond what can be achieved with more established metric-based, subtraction-type methods.