At specific growth rates above a particular critical value, Crabtree-positive microorganisms exceed their respiratory capacity and enter diauxic growth metabolism. Excess substrate is converted reductively to an overflow metabolite, resulting in decreased biomass yield and productivity. To prevent this scenario, the cells can be cultivated in a fed-batch mode at a growth rate maintained below the critical value, µcrit. This approach entails two major challenges: accurately estimating the current specific growth rate and controlling it successfully over the course of the fermentation. In this work, the specific growth rate of S. cerevisiae and E. coli was estimated from enhanced on-line biomass concentration measurements obtained with dielectric spectroscopy and turbidity. A feedforward-feedback control scheme was implemented to maintain the specific growth rate at a setpoint below µcrit, while on-line FTIR measurements provided the early detection of the overflow metabolites. The proposed approach is in line with the principles of Bioprocess Analytical Technology (BioPAT), and provides a means to increase the productivity of Crabtree-positive microorganisms.