Part of the Research and Development program concerning high level nuclear waste (HLW) glasses aims to assess new glass formulations able to incorporate a high waste content with enhanced properties in terms of thermal stability, chemical durability, and process ability. This study focuses on peraluminous glasses of the SiO2 – Al2O3 – B2O3 – Na2O – Li2O – CaO – La2O3 system, defined by an excess of aluminum ions Al3+ in comparison with modifier elements such as Na+, Li+ or Ca2+. To understand the effect of composition on physical properties of glasses (viscosity, density, Tg), a Design Of Experiments (DOE) approach was applied to investigate the peraluminous glass domain. The influence of each oxide was quantified to build predictive models for each property. Lanthanum and lithium oxides appear to be the most influential factors on peraluminous glass properties. •A Design of Experiment approach to link composition and glass properties.•Adding alkali decreases glass transition temperature.•Adding La2O3 strongly decreases glass melt viscosity.•Adding La2O3 increases density.