  The Gaia-ESO Survey (GES) is a large public spectroscopic survey which
acquired spectra for more than 100000 stars across all major components of the
Milky Way. In addition to atmospheric parameters and stellar abundances that
have been derived in previous papers of this series, the GES spectra allow us
to detect spectroscopic binaries with one (SB1), two (SB2) or more (SBn $\ge$
3) components. Cross-correlation functions (CCFs) have been re-computed thanks
to a dozen spectral masks probing a range of effective temperatures, surface
gravities and metallicities. By optimising the mask choice for a given
spectrum, the new computed so-called Nacre (Narrow cross-correlation
experiment) CCFs are narrower and allow to unblend more stellar components than
standard masks. The Doe (Detection of Extrema) extremum-finding code then
selects the individual components and provides their radial velocities. From
the sample of HR10 and HR21 spectra corresponding to 37565 objects, the present
study leads to the detection of 322 SB2, ten (three of them being tentative)
SB3, and two tentative SB4. In particular, compared to our previous study, the
Nacre CCFs allow us to multiply the number of SB2 candidates by $\approx$ 1.5.
The colour-magnitude diagram reveals, as expected, the shifted location of the
SB2 main sequence. A comparison between the SB identified in Gaia DR3 and the
ones detected in the present work is performed and the complementarity of the
two censuses is discussed. An application to mass-ratio determination is
presented, and the mass-ratio distribution of the GES SB2 is discussed. When
accounting for the SB2 detection rate, an SB2 frequency of $\approx$ 1.4% is
derived within the present stellar sample of mainly FGK-type stars. As primary
outliers identified within the GES data, SBn spectra produce a wealth of
information and useful constraints for the binary population synthesis studies.
