Bistable perception refers to a broad class of dynamically alternating visual illusions that result from ambiguous images. These illusions provide a powerful method to study the mechanisms that determine how visual input is integrated over space and time. Binocular rivalry occurs when subjects view different images in each eye, and a similar experience called stimulus rivalry occurs even when the left and right images are exchanged at a fast rate. Many previous studies have identified with fMRI a network of cortical regions that are recruited during binocular rivalry, relative to non-rivalrous control conditions (termed replay) that use physically changing stimuli to mimic rivalry. However, we show here for the first time that additional cortical areas are activated when subjects experience rivalry with interocular grouping. When interocular grouping occurs, activation levels broadly increase, with a slight shift towards right hemisphere lateralization. Moreover, direct comparison of binocular rivalry with and without grouping highlights strong focused activity in the intraparietal sulcus and lateral occipital areas, such as right-sided retinotopic visual areas LO1 and IP2, as well as activity in left-sided visual areas LO1, and IP0-IP2. The equivalent analyses for comparable stimulus (eye-swap) rivalry showed very similar results; the main difference is greater recruitment of the right superior parietal cortex for binocular rivalry, as previously reported. Thus, we found minimal interaction between the novel networks isolated here for interocular grouping, and those previously attributed to stimulus and binocular rivalry. We conclude that spatial integration (i.e,. image grouping/segmentation) is a key function of lateral occipital/intraparietal cortex that acts similarly on competing binocular stimulus representations, regardless of fast monocular changes.