In deep learning-based image classification, it is necessary to achieve high generalization performance while suppressing overfitting in situations when training data are limited. Mixup, a data augmentation using linear interpolation in the input space, is effective in smoothing the decision boundary, but it can hinder the model’s ability to learn fine-grained, class-specific details in the later training stages. On the other hand, augmentation by First-Order Manifold Augmentation (FOMA) utilizes local geometry but is designed for regression, making its direct application to classification difficult. We propose a two-phase augmentation method that changes its strategy according to the phase of training. In Phase 1, standard Mixup is used for global interpolation to smooth the class boundary. In Phase 2, we apply Local-FOMA, which is designed for classification, to estimate principal component directions based on local neighborhoods in the feature space and perform data augmentation while preserving the manifold structure. The weights of the loss function are linearly transitioned during the learning process, enabling a smooth switch from Mixup to Local-FOMA. On CIFAR-100 and CIFAR-10, our method outperformed strong Mixup variants. Under distribution shifts (CIFAR-C), it also improves robustness and was particularly effective on CIFAR-100-C, suggesting that the method is particularly advantageous in complex scenarios involving datasets with many classes. These results demonstrate that Mixup-FOMA provides an effective strategy to enhance both classification performance and robustness by gradually combining global generalization with local refinement.