  The nature of a substantial percentage (about one fifth) of hard X-ray
sources discovered with the BAT instrument onboard the Neil Gehrels Swift
Observatory (hereafter Swift) is unknown because of the lack of an identified
longer-wavelength counterpart. Without such follow-up, an X-ray catalogue is of
limited astrophysical value: we therefore embarked, since 2009, on a long-term
project to uncover the optical properties of sources identified by Swift by
using a large suite of ground-based telescopes and instruments. In this work,
we continue our programme of characterization of unidentified or poorly studied
hard X-ray sources by presenting the results of an optical spectroscopic
campaign aimed at pinpointing and classifying the optical counterparts of 35
hard X-ray sources taken from the 70-month BAT catalogue. (...) With the use of
optical spectra taken at six different telescopes we were able to identify the
main spectral characteristics (continuum type, redshift, and emission or
absorption lines) of the observed objects, and determined their nature. We
identify and characterize a total of 41 optical candidate counterparts
corresponding to 35 hard X-ray sources given that, because of positional
uncertainties, multiple lower energy counterparts can sometimes be associated
with higher energy detections. We discuss which ones are the actual (or at
least most likely) counterparts based on our observational results. In
particular, 31 sources in our sample are active galactic nuclei: 16 are
classified as Type 1 (with broad and narrow emission lines) and 13 are
classified as Type 2 (with narrow emission lines only); two more are BL
Lac-type objects. We also identify one LINER, one starburst, and 3 elliptical
galaxies. The remaining 5 objects are galactic sources: we identify 4 of them
as cataclysmic variables, whereas one is a low mass X-ray binary.
