  We investigate the prospects of electromagnetic follow-up observations for
binary neutron star (BNS) mergers, with the help of early warnings from
decihertz gravitational-wave (GW) observatories, B-DECIGO and DO-Optimal.
Extending the previous work, we not only give quick assessments of joint short
$\gamma$-ray burst (sGRB) detection rates for different $\gamma$-ray satellites
and BNS population models, but also elaborate on the analyses and results on
multi-band kilonova detections for survey telescopes with different limiting
magnitudes. During an assumed 4-year mission time for decihertz GW
observatories, we find that for the goals of electromagnetic follow-ups,
DO-Optimal performs better than B-DECIGO as a whole on the detection rate, and
has a larger detectable distance for joint sGRB/kilonova searches. Taking the
log-normal population model for BNS mergers and a one-day early-warning time as
an example, we discuss the accuracy in localization and timing, as well as the
redshift distributions for various synergy observations with electromagnetic
facilities and decihertz GW detectors. Based on our analyses, we propose a
feasible "wait-for" pattern as a novel detecting mode for future
multi-messenger astrophysics.
