  Joint multi-messenger observations with gravitational waves and
electromagnetic data offer new insights into the astrophysical studies of
compact objects. The third Advanced LIGO and Advanced Virgo observing run began
on April 1, 2019; during the eleven months of observation, there have been 14
compact binary systems candidates for which at least one component is
potentially a neutron star. Although intensive follow-up campaigns involving
tens of ground and space-based observatories searched for counterparts, no
electromagnetic counterpart has been detected. Following on a previous study of
the first six months of the campaign, we present in this paper the next five
months of the campaign from October 2019 to March 2020. We highlight two
neutron star - black hole candidates (S191205ah, S200105ae), two binary neutron
star candidates (S191213g and S200213t) and a binary merger with a possible
neutron star and a "MassGap" component, S200115j. Assuming that the
gravitational-wave candidates are of astrophysical origin and their location
was covered by optical telescopes, we derive possible constraints on the matter
ejected during the events based on the non-detection of counterparts. We find
that the follow-up observations during the second half of the third observing
run did not meet the necessary sensitivity to constrain the source properties
of the potential gravitational-wave candidate. Consequently, we suggest that
different strategies have to be used to allow a better usage of the available
telescope time. We examine different choices for follow-up surveys to optimize
sky localization coverage vs.\ observational depth to understand the likelihood
of counterpart detection.
