We identify close companions of brightest cluster galaxies (BCGs) for the purpose of quantifying the rate at which these galaxies grow via mergers. By exploiting deep photometric data from the Canada–France–Hawaii Telescope Legacy Survey (CFHTLS), we probe the number of companions per BCG (Nc) with luminosity ratios down to those corresponding to potential minor mergers of 20:1. We also measure the average luminosity in companions per galaxy (Lc). We find that Nc and Lc rise steeply with luminosity ratio for both the BCGs, and a control sample of other bright, red, cluster galaxies. The trend for BCGs rises more steeply, resulting in a larger number of close companions. For companions within 50 kpc of a BCG, Nc = 1.38 ± 0.14 and Lc = 2.14 ± 0.31 × 1010 L⊙, and for companions within 50 kpc of a luminosity matched control sample of non-BCGs, Nc = 0.87 ± 0.08 and Lc = 1.48 ± 0.20 × 1010 L⊙. This suggests that the BCGs are likely to undergo more mergers compared to otherwise comparable luminous galaxies. Additionally, compared to a local sample of luminous red galaxies, the more distant sample presented in this study (with redshifts between 0.15 and 0.39) shows a higher Nc, suggesting that the younger and smaller BCGs are still undergoing hierarchical formation. Using the Millennium Simulations we model and estimate the level of contamination due to unrelated cluster galaxies. The contamination by interloping galaxies is 50 per cent within projected separations of 50 kpc, but within 30 kpc, 60 per cent of identified companions are real physical companions. We conclude that the luminosity of bound merger candidates down to luminosity ratios of 20:1 could be adding as much as 10 per cent to the mass of a typical BCG over 0.5 Gyr at redshifts of z ∼ 0.3.