Evaluating the genotype (G) by management practice (M) interaction in agronomic experimentation is essential to help grain growers optimise the desired trait of interest (e.g. grain yield). However, the approach is complicated by interaction effects with environmental factors that differ across sites and seasons. Popular statistical methods for modelling the genotype by environment (G × E) interaction are limited as they neither provide a biological understanding of how environmental factors impact on the G × E interaction, nor assess how different management practices influence the G × E interaction. These limitations may be addressed by incorporating environmental covariates (ECs) into the modelling process to better explain why differences exist in the optimal genotype by management practice combination across environments. A novel statistical methodology is proposed that incorporates ECs to explore genotype by environment by management practice (G × E × M) interactions in agronomic multi-environment trial studies. A predictive linear mixed model is proposed that incorporates site and season specific ECs into a commonly used G × E interaction framework. The model is extended to include the effect of continuously varying agronomic management practices, whilst allowing for non-linear trait responses and complex variance structures. The methodology is applied to a multi-environment dataset exploring yield response to established plant density in a series of sorghum agronomy trials. Results indicated that the grain yield of sorghum genotypes would be optimised in environments that have (i) high total plant available water and photo-thermal quotient around flowering, (ii) low pre-flowering radiation and evapotranspiration and (iii) achieved flowering at an optimal time. Under this set of optimal G × E conditions, a high established plant density further optimised grain yield. The proposed methodology successfully incorporated ECs to better understand G × E × M interactions in agronomic field trials, enabling predictions to be made in an untested or future environment and linking the statistical analysis to crop-ecophysiology principles. This work will improve the generalisations agronomists can draw from experimental studies, enhancing the biological understanding of the analysis results and allowing for the development of more targeted and robust recommendations for agronomic practices. •Incorporates environmental covariates and management in the statistical analysis.•Can identify key environmental covariates contributing to the G × E × M interaction.•Non-linear trait response to an environmental covariate can be modelled.•Environmental covariates can predict performance in future environments.