Abstract The most promising variation of the standard siren technique combines gravitational-wave (GW) data for binary neutron star (BNS) mergers with redshift measurements enabled by their electromagnetic (EM) counterparts, to constrain cosmological parameters such as H 0 , Ω m , and w 0 . Here we evaluate the near- and long-term prospects of multimessenger cosmology in the era of future GW observatories: Advanced LIGO Plus (A+, 2025), Voyager-like detectors (2030s), and Cosmic Explorer–like detectors (2035 and beyond). We show that the BNS horizon distance of ≈ 700 Mpc for A+ is well matched to the sensitivity of the Vera C. Rubin Observatory (VRO) for kilonova detections. We find that one year of joint A+ and VRO observations will constrain the value of H 0 to percent-level precision, given a small investment of VRO time dedicated to target-of-opportunity GW follow-up. In the Voyager era, the BNS–kilonova observations begin to constrain Ω m with an investment of a few percent of VRO time. With the larger BNS horizon distance in the Cosmic Explorer era, on-axis short gamma-ray bursts (SGRBs) and their afterglows (though accompanying only some of the GW-detected mergers) supplant kilonovae as the most promising counterparts for redshift identification. We show that five years of joint observations with Cosmic Explorer–like facilities and a next-generation gamma-ray satellite with localization capabilities similar to that presently possible with Swift could constrain both Ω m and w 0 to 15%–20%. We therefore advocate for a robust target-of-opportunity (ToO) program with VRO, and a wide-field gamma-ray satellite with improved sensitivity in the 2030s, to enable standard siren cosmology with next-generation gravitational-wave facilities.