ABSTRACTGlobular clusters exhibit abundance variations, defining ‘multiple populations’, which have prompted a protracted search for their origin. Properties requiring explanation include the high fraction of polluted stars (∼40−90 per cent, correlated with cluster mass), the absence of pollution in young clusters, and the lower pollution rate with binarity and distance from the cluster centre. We present a novel mechanism for late delivery of pollutants into stars via accretion of substellar companions. In this scenario, stars move through a medium polluted with asymptotic giant branch (AGB) and massive star ejecta, accreting material to produce companions with typical mass ratio q ∼ 0.1. These companions undergo eccentricity excitation due to dynamical perturbations by passing stars, culminating in a merger with their host star. The accretion of the companion alters surface abundances via injected pollutant. Alongside other self-enrichment models, the companion accretion model can explain the dilution of pollutant and correlation with intracluster location. The model also explains the ubiquity and discreteness of the populations and correlations of enrichment rates with cluster mass, cluster age, and stellar binarity. Abundance variations in some clusters can be broadly reproduced using AGB and massive binary ejecta abundances from the literature. In other clusters, some high companion mass ratios (q ≳ 1) are required. In these cases, the available mass budget necessitates a variable degree of mixing of the polluted material with the primary star, deviations from model ejecta abundances, or mixing of internal burning products. We highlight the avenues of further investigation that are required to explore some of the key processes invoked in this model.