Open-set domain generalization addresses a real-world challenge: training a model to generalize across unseen domains (domain generalization) while also detecting samples from unknown classes not encountered during training (open-set recognition). However, most existing approaches tackle these issues separately, limiting their practical applicability. To overcome this limitation, we propose a unified framework for open-set domain generalization by introducing Feature-space Semantic Invariance (FSI). FSI maintains semantic consistency across different domains within the feature space, enabling more accurate detection of OOD instances in unseen domains. Additionally, we adopt a generative model to produce synthetic data with novel domain styles or class labels, enhancing model robustness. Initial experiments show that our method improves AUROC by 9.1% to 18.9% on ColoredMNIST, while also significantly increasing in-distribution classification accuracy.