A search for decays of the Higgs and Z boson to pairs of or (n = 1, 2, 3) mesons, with their subsequent decay to pairs, is presented. The analysis uses data from proton-proton collisions at , collected with the CMS detector at the LHC in 2017 and corresponding to an integrated luminosity of 37.5. While an observation of such a decay with this sample would indicate the presence of physics beyond the standard model, no significant excess is observed. Upper limits at 95% confidence level are placed on the branching fractions of these decays. In the pair channel, the limits are and for the Higgs and Z boson, respectively, while in the combined pair channel, the limits are and , respectively, when the mesons from the Higgs and Z boson decay are assumed to be unpolarized. When fully longitudinal and transverse polarizations are considered the limits reduce by about 22–29% and increase by about 10–13%, respectively.