The previous analysis of the ANTARES all-flavour 12-year neutrino data sample provided the observation of an excess of events, at the highest energies, above the expected atmospheric foregrounds. This excess, even though mild (1.8 sigma), has been found to be consistent in spectral slope and normalisation with the high-energy diffuse cosmic neutrino signal detected by the IceCube Neutrino Observatory. Even though the smaller detector size does not provide sufficient statistics to claim an independent discovery, the analysis of ANTARES data can provide valuable information in the study of the high-energy neutrino signal, in particular for what concerns the details of its energy distribution in the case of soft-spectra solutions. To improve the previous ANTARES results, a new event selection has been developed for cascade-like events, relying on a Boosted Decision Tree multivariate-analysis technique. This increased the event statistics in this channel by a factor of 5, while also dramatically reducing the surviving foregrounds and the related systematic uncertainties. This contribution will report on the status of the analysis and the prospects emerging from the use of this new event sample in the search for a diffuse flux of cosmic neutrinos.