In this work, we propose PSScreen V2, a partially supervised self-training framework for multiple retinal disease screening. Unlike previous methods that rely on fully labelled or single-domain datasets, PSScreen V2 is designed to learn from multiple partially labelled datasets with different distributions, addressing both label absence and domain shift challenges. To this end, PSScreen V2 adopts a three-branch architecture with one teacher and two student networks. The teacher branch generates pseudo labels from weakly augmented images to address missing labels, while the two student branches introduce novel feature augmentation strategies: Low-Frequency Dropout (LF-Dropout), which enhances domain robustness by randomly discarding domain-related low-frequency components, and Low-Frequency Uncertainty (LF-Uncert), which estimates uncertain domain variability via adversarially learned Gaussian perturbations of low-frequency statistics. Extensive experiments on multiple in-domain and out-of-domain fundus datasets demonstrate that PSScreen V2 achieves state-of-the-art performance and superior domain generalization ability. Furthermore, compatibility tests with diverse backbones, including the vision foundation model DINOv2, as well as evaluations on chest X-ray datasets, highlight the universality and adaptability of the proposed framework. The codes are available at https://github.com/boyiZheng99/PSScreen_V2.