  We present a study of the [OIII]5007/[OII]3727 (O32) ratios of star-forming
galaxies drawn from MUSE data spanning a redshift range 0.28<z<0.85. Recently
discovered Lyman continuum (LyC) emitters have extremely high oxygen line
ratios: O32>4. Here we aim to understand the properties and the occurrences of
galaxies with such high line ratios. Combining data from several MUSE 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 O32 ratios (3.7%) and 104 galaxies have O32>1 (26%). Our analysis shows
no significant correlation between M*, SFR, and the distance from the SFR-M*
relation with O32. We find a decrease in the fraction of galaxies with O32>1
with increasing M*, however, this is most likely a result of the relationship
between O32 and metallicity, rather than between O32 and M*. We draw a
comparison sample of local analogues with <z>~0.03 from SDSS, and find similar
incidence rates for this sample. In order to investigate the evolution in the
fraction of high O32 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. Finally, based on a comparison between
electron temperature estimates from the [OIII4363]/[OIII]5007 ratio of the
extreme oxygen emitters and nebular models, we argue that the galaxies with the
most extreme O32 ratios have young light-weighted ages.
