Cumulative multi-messenger detection rates as a function of redshift (luminosity distance) for our fiducial NSNS and BHNS population (SFHo EoS, non-spinning BHs), assuming the ET triangle 10 km configuration. Left panel: NSNS population. The light grey line (“All NSNS”) represents the intrinsic merger rate for the NSNS population, with the grey band showing its uncertainty due to that on the local merger rate. This uncertainty propagates as a constant relative error to all the other rates. The black (“GW ET”) line is the cumulative GW detection rate (events per year with network S/N ≥ 12). The blue (“Kilonova+GW”), red (“Afterglow+GW”), purple (“Afterglow VHE+GW”) and orange (“Prompt+GW”) lines are the cumulative detection rates for the joint detection of ET GW plus a KN (g band), a GRB afterglow (radio and VHE bands), or a GRB prompt (the orange and purple lines account, respectively, for the Fermi/GBM and CTA duty cycle and field of view). The dashed lines are the cumulative detection rates assuming only the binaries with ΔΩ_90% < 100 deg². The assumed thresholds or instruments sensitivity are shown in the legend. Right panel: Same as the left panel but for the BHNS population.