In this paper we present an in-depth analysis of a recently proposed Standard Model extension with a complete fourth generation of quarks and leptons, which are vector-like with respect to the Standard Model gauge group and charged under a new spontaneously broken vector-like U(1) gauge symmetry. The model is designed to explain the known muon anomalies, i.e. the observed deviations from Standard Model predictions in the anomalous magnetic moment of the muon, ∆a µ , and in b → s + − processes. We perform a global χ 2 analysis of the data with 65 model parameters and including 98 observables. We find many points with χ 2 per degree of freedom ≤ 1. The vector-like leptons and the new heavy Z are typically much lighter than a TeV and would, thus, be eminently visible at the HL-LHC.