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We find three previously unknown companions for <jats:italic>\u03b8<\/jats:italic><jats:sup>1<\/jats:sup> Ori B, <jats:italic>\u03b8<\/jats:italic><jats:sup>2<\/jats:sup> Ori B, and <jats:italic>\u03b8<\/jats:italic><jats:sup>2<\/jats:sup> Ori C. We determined a separation for the previously suspected companion of NU Ori. We confirm four companions for <jats:italic>\u03b8<\/jats:italic><jats:sup>1<\/jats:sup> Ori A, <jats:italic>\u03b8<\/jats:italic><jats:sup>1<\/jats:sup> Ori C, <jats:italic>\u03b8<\/jats:italic><jats:sup>1<\/jats:sup> Ori D, and <jats:italic>\u03b8<\/jats:italic><jats:sup>2<\/jats:sup> Ori A, all with substantially improved astrometry and photometric mass estimates. We refined the orbit of the eccentric high-mass binary <jats:italic>\u03b8<\/jats:italic><jats:sup>1<\/jats:sup> Ori C and we are able to derive a new orbit for <jats:italic>\u03b8<\/jats:italic><jats:sup>1<\/jats:sup> Ori D. We find a system mass of 21.7 <jats:italic>M<\/jats:italic><jats:sub>\u2299<\/jats:sub> and a period of 53 days. Together with other previously detected companions seen in spectroscopy or direct imaging, eleven of the 16 high-mass stars are multiple systems. We obtain a total number of 22 companions with separations up to 600 AU. The companion fraction of the early B and O stars in our sample is about two, significantly higher than in earlier studies of mostly OB associations. The separation distribution hints toward a bimodality. Such a bimodality has been previously found in A stars, but rarely in OB binaries, which up to this point have been assumed to be mostly compact with a tail of wider companions. We also do not find a substantial population of equal-mass binaries. The observed distribution of mass ratios declines steeply with mass, and like the direct star counts, indicates that our companions follow a standard power law initial mass function. Again, this is in contrast to earlier findings of flat mass ratio distributions in OB associations. 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