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We present a study of the [O III]/[O II] ratios of star-forming galaxies drawn from Multi-Unit Spectroscopic Explorer (MUSE) data spanning a redshift range 0.28 < z < 0.85. Recently discovered Lyman continuum (LyC) emitters have extremely high oxygen line ratios: [O III]lambda 5007/[O II]lambda lambda 3726, 3729 > 4. Here we aim to understand the properties and the occurrences of galaxies with such high line ratios. Combining data from several MUSE Guaranteed Time Observing (GTO) programmes, we select a population of star-forming galaxies with bright emission lines, from which we draw 406 galaxies for our analysis based on their position in the z-dependent star formation rate (SFR) stellar mass (M*) plane. Out of this sample 15 are identified as extreme oxygen emitters based on their [O III]/[O II] ratios (3.7%) and 104 galaxies have [O III]/[O II] > 1 (26%). Our analysis shows no significant correlation between M*, SFR, and the distance from the SFR M, relation with [O III]/[O II]. We find a decrease in the fraction of galaxies with [O III]/[O II] > 1 with increasing M*, however, this is most likely a result of the relationship between [O III]/[O II] and metallicity, rather than between [O III]/[O II] and M. We draw a comparison sample of local analogues with < z > 0.03 from the Sloan Digital Sky Survey, and find similar incidence rates for this sample. In order to investigate the evolution in the fraction of high [O III]/[O II] emitters with redshift, we bin the sample into three redshift subsamples of equal number, but find no evidence for a dependence on redshift. Furthermore, we compare the observed line ratios with those predicted by nebular models with no LyC escape and find that most of the extreme oxygen emitters can be reproduced by low metallicity models. The remaining galaxies are likely LyC emitter candidates.