Perceptual multistability is well-known and mostly visually demonstrated: Common examples are Necker's cube or Rubin's face-vase that produce qualitatively different percepts continuously oscillating between the solutions despite physically stable stimuli. We lack knowledge about similar phenomena in other domains, for instance in linguistics, where we are faced with homonyms that create multistability of cognitive semantics, differently assigned meanings of identical words. Our participants listened to repeated presentations of homonyms for which two or even three meanings could be assigned, and they reported the dominant meaning perceived at a certain point in time. Results showed that most participants experienced multistability of meaning for homonyms, with semiperiodic changes in dominant meaning similar to multistabity in perception. These findings suggest that multistability is a general property of the brain's neural architecture that resolves ambiguity irrespective of the level of representation.