A combined statistical analysis of searches for heavy vector boson resonances decaying into pairs of W, Z, or Higgs bosons, as well as into quark pairs (qq, bb, tt, tb) or lepton pairs (ℓ⁺ℓ⁻, ℓν), with ℓ = e, μ, τ, is presented. The results are based on proton-proton collision data at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb−1, collected by the CMS experiment from 2016 to 2018. No significant deviation from the expectations of the standard model is observed. The results are interpreted in the simplified heavy vector triplet (HVT) framework, setting 95% confidence level upper limits on the production cross sections and on the coupling strengths of the HVT bosons to standard model particles. The results exclude HVT resonances with masses below 5.5 TeV in a weakly coupled scenario, below 4.8 TeV in a strongly coupled scenario, and up to 2.0 TeV in the case of production via vector boson fusion. The combination provides the most stringent constraints to date on new phenomena predicted by the HVT model.