  In this study, we revisit 32 planetary systems around evolved stars observed
within the framework of the Okayama Planet Search Program and its collaborative
framework of the EAPS-Net to search for additional companions and investigate
the properties of stars and giant planets in multiple-planet systems. With our
latest radial velocities obtained from Okayama Astrophysical Observatory (OAO),
we confirm an additional giant planet in the wide orbit of 75 Cet system
($P_{\rm{c}} = 2051.62_{-40.47}^{+45.98}\ \rm{d}$, $M_{\rm{c}}\sin
i=0.912_{-0.090}^{+0.088}\ M_{\rm{J}}$, and
$a_{\rm{c}}=3.929_{-0.058}^{+0.052}\ \rm{au}$), along with five stars
exhibiting long-term radial velocity accelerations, which indicates massive
companions in the wide orbits. We have also found that the radial velocity
variations of several planet-harboring stars may indicate additional planet
candidates, stellar activities, or other understudied sources. These stars
include $\epsilon$ Tau, 11 Com, 24 Boo, 41 Lyn, 14 And, HD 32518, and $\omega$
Ser. We further constrain the orbital configuration of the HD 5608, HD 14067,
HD 120084, and HD 175679 systems by combining radial velocities with
astrometry, as their host central stars exhibit significant astrometric
accelerations. For other systems, we simply refine their orbital parameters.
Moreover, our study indicates that the OPSP planet-harboring stars are more
metal-poor compared to the currently known planet-harboring stars, and this is
likely due to the $B-V$ color upper limit at 1.0 for star selection in the
beginning of the survey. Finally, by investigating the less-massive giant
planets ($< 5 M_{\rm{J}}$) around currently known planet-harboring evolved
stars, we have found that metallicity positively correlates with the
multiplicity and total planet mass of the system, which can be evidence for the
core-accretion planet formation model.
