We perform a phenomenological analysis of simplified models of light, feebly interacting particles (FIPs) that can provide a combined explanation of the anomalies in b → sl+l− transitions at LHCb and the anomalous magnetic moment of the muon. Different scenarios are categorised according to the explicit momentum dependence of the FIP coupling to the b−s and μ−μ vector currents and they are subject to several constraints from flavour and precision physics. We show that viable combined solutions to the muon g − 2 and flavour anomalies exist with the exchange of a vector FIP with mass larger than 4 GeV. Interestingly, the LHC has the potential to probe this region of the parameter space by increasing the precision of the Z → 4μ cross-section measurement. Conversely, we find that solutions based on the exchange of a lighter vector, in the mV < 1 GeV range, are essentially excluded by a combination of B → K+ invisible and W-decay precision bounds
