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The re-identification (ReID) of individuals over a complex network of cameras is a challenging task, especially under real-world surveillance conditions. Several deep learning models have been proposed for visible-infrared (V-I) person ReID to recognize individuals from images captured using RGB and IR cameras. However, performance may decline considerably if RGB and IR images captured at test time are corrupted (e.g., noise, blur, and weather conditions). Although various data augmentation (DA) methods have been explored to improve the generalization capacity, these are not adapted for V-I person ReID. In this paper, a specialized DA strategy is proposed to address this multimodal setting. Given both the V and I modalities, this strategy allows to diminish the impact of corruption on the accuracy of deep person ReID models. Corruption may be modality-specific, and an additional modality often provides complementary information. Our multimodal DA strategy is designed specifically to encourage modality collaboration and reinforce generalization capability. For instance, punctual masking of modalities forces the model to select the informative modality. Local DA is also explored for advanced selection of features within and among modalities. The impact of training baseline fusion models for V-I person ReID using the proposed multimodal DA strategy is assessed on corrupted versions of the SYSU-MM01, RegDB, and ThermalWORLD datasets in terms of complexity and efficiency. Results indicate that using our strategy provides V-I ReID models the ability to exploit both shared and individual modality knowledge so they can outperform models trained with no or unimodal DA. GitHub code: https://github.com/art2611/ML-MDA.