Abstract A new thermodynamic model for silicate melt in the Na2O–CaO–K2O–FeO–MgO–Al2O3–SiO2–TiO2–Fe2O3–Cr2O3 model system is presented, building on the tholeiitic through to granitic melt model of Holland et al. (2018) [Journal of Petrology, 59, 881–900] but extending for the first time into anhydrous alkaline systems. The new melt model is accompanied by new thermodynamic models for nepheline, kalsilite, leucite, melilite and ilmenite. Collectively these models enable pseudosection modelling of alkaline-silicate magmatic systems, providing a new tool for investigating this geologically- and economically-important compositional space. The models are calibrated with respect to experimental data on phase relations among minerals and melt, and the fit is benchmarked here via detailed comparison with seven experimental datasets, which encompass a range of pressure (0–22 kbar), temperature (680–1350°C), oxygen fugacity (log fO2 ΔFMQ-3 to +1), total alkali (3–16 wt %) and silica (37–70 wt %) conditions. The calculated pseudosections successfully reproduce experimental crystallisation sequences and phase compositions, indicating that the thermodynamic models are well calibrated across this spectrum of conditions. Redox buffered experimental conditions are simulated using oxygen buffered pseudosections. Contouring of oxygen buffered pseudosections with XFe3+ (mol. Fe3+/Fetotal), or pseudosections of varying XFe3+ with ΔFMQ, reveals (i) often complex and non-intuitive relationships between these two representations of oxidation state, and (ii) substantial variation in ferric iron over narrow temperature intervals in some oxygen buffered sets of experiments. An implication is that simulating oxygen buffering is vital when benchmarking thermodynamic models using experimental results. Furthermore, because natural igneous systems likely feature a near-constant XFe3+, it is important to assess experimental results in this framework when making inferences about natural systems, recognising that oxygen fugacity is a consequence not a control of phase equilibria in nature. Overall, our new models provide a novel tool to explore the role of variables, such as pressure, fractional crystallisation and crustal assimilation in the petrogenesis of alkaline-silicate magmatic systems and their associated mineralisation.