Increasing the magnesium (Mg) concentration of vegetables (biofortification) will often require ‘luxury’ uptake where the whole-plant concentration of Mg (cp) is greater than required for maximum yield. Our aim was to quantify some of the physiological factors influencing luxury uptake of Mg to aid subsequent development of agronomic techniques for biofortification. Peas, Pisum sativum, were used as a test species. A sand culture experiment related vegetative growth and cp for plants grown with a range of Mg and potassium (K) supply rates. We developed a model of Mg uptake including feedback control exerted by cp. The model was parameterised with results from a solution culture experiment and then used to explore ways to increase luxury uptake of Mg. Feedback control of Mg uptake by cp was weak. Biomass did not increase if the Mg concentration exceeded 0.11% in the whole plant or 0.13% in the shoots. Values obtained in the field are often larger than this. Our results indicate that luxury uptake of Mg by peas is readily achieved, provided that there is ample supply of Mg2+ to the root surfaces. In field soils though, transport of Mg2+ to the roots may limit uptake and cation exchange processes restrict the ability of Mg fertilisers to substantially increase Mg uptake. Increasing root growth will usually increase Mg uptake, but cp may not rise if biomass is also increased.