The results of a model-independent search for the pair production of new bosons within a mass range of 0.21 < m < 60 GeV, are presented. This study utilizes events with a four-muon final state. We use two data sets, comprising 41.5 fb(-1) and 59.7 fb(-1) of proton-proton collisions at root s = 13TeV, recorded in 2017 and 2018 by the CMS experiment at the CERN LHC. The study of the 2018 data set includes a search for displaced signatures of a new boson within the proper decay length range of 0 < c tau < 100mm. Our results are combined with a previous CMS result, based on 35.9 fb(-1) of proton-proton collisions at root s = 13TeV collected in 2016. No significant deviation from the expected background is observed. Results are presented in terms of a model-independent upper limit on the product of cross section, branching fraction, and acceptance. The findings are interpreted across various benchmark models, such as an axion-like particle model, a vector portal model, the next-to-minimal supersymmetric standard model, and a dark supersymmetric scenario, including those predicting a non-negligible proper decay length of the new boson. In all considered scenarios, substantial portions of the parameter space are excluded, expanding upon prior results.