The joint detection of GW170817 and GRB 170817A opened the era of multi-messenger astronomy with gravitational waves (GWs) and provided the first direct probe that at least some binary neutron star (BNS) mergers are progenitors of short gamma-ray bursts (S-GRBs). In the next years, we expect to have more multi-messenger detections of BNS mergers, thanks to the increasing sensitivity of GW detectors. Here, we present a comprehensive study on the prospects for joint GW and electromagnetic observations of merging BNSs in the fourth LIGO–Virgo–KAGRA observing run with Fermi, Swift, INTEGRAL and SVOM. This work combines accurate population synthesis models with simulations of the expected GW signals and the associated S-GRBs, considering different assumptions about the GRB jet structure. We show that the expected rate of joint GW and electromagnetic detections could be up to ∼ 6 yr−1 when Fermi/GBM is considered. Future joint observations will help us to better constrain the association between BNS mergers and S-GRBs, as well as the geometry of the GRB jets.