Joint analysis of multi-omic single-cell data across cohorts has significantly enhanced the comprehensive analysis of cellular processes. However, most of the existing approaches for this purpose require access to samples with complete modality availability, which is impractical in many real-world scenarios. In this paper, we propose (Single-Cell Cross-Cohort Cross-Category) integration, a novel framework that learns unified cell representations under domain shift without requiring full-modality reference samples. Our generative approach learns rich cross-modal and cross-domain relationships that enable imputation of these missing modalities. Through experiments on real-world multi-omic datasets, we demonstrate that offers a robust solution to single-cell tasks such as cell type clustering, cell type classification, and feature imputation.