Multistable perception phenomena have been widely used for examining visual awareness and its underlying cortical mechanisms. Plausible models can explain binocular rivalry – the perceptual switching between two conflicting stimuli presented to each eye. Human subjects also report rivalry between percepts formed by grouping complementary patches from images presented to either eye. The dynamics of rivalry between such integrated percepts is not completely understood, and it is unclear whether models that explain binocular rivalry can be generalized. Classical models rely on mutual inhibition between distinct populations whose activity corresponds to each percept, with switches driven by adaptation or noise. Such models do not reflect the more complex patterns of neural activity necessary to describe interocular grouping. Moreover, the switching dynamics between more than two percepts is characterized by the sequence of perceptual states in addition to dominance times. Mechanistic models of multistable rivalry need to explain such dynamics. We studied the effect of color saturation on the dynamics of four-state perceptual rivalry. We presented subjects with split-grating stimuli composed of a half green grating and half red orthogonal grating to each eye. Subjects reliably reported four percepts: the two stimuli presented to each eye, as well as two coherent images resulting form interocular grouping. We hypothesized that an increase in color saturation would provide a strong cue to group the coherent halves, and would increase the dominance of grouped percepts. Experiments confirmed that this was the case. Further analysis showed that the increase in the fraction of time grouped stimuli were perceived was partly due to a decrease in single-eye dominance durations and partly due to an increase in the number of visits to grouped percepts. We used a computational model to show that our experimental observations can be reproduced by combining three mechanisms: mutual inhibition, recurrent excitation, and adaptation.