Graph learning has shown significant advantages in organizing and leveraging complex data, making it promising for numerous real-world applications with heterogeneous information, particularly multi-omics data analysis. Despite its potential in such scenarios, existing methods are still in their infancy, lacking architectural potential and struggling to handle such complex data. In this paper, we propose the Multiplex Mixture of Graph Learners (MMoG) framework. MMoG first conducts fine-grained processing of consensus and unique information, constructing consistent features and multiplex graph structures. Then, a macroscopically shared group of sub-GNNs with diverse orders and architectures synergistically learn representations, providing a foundation for strong interaction between different views. Inspired by the mixture of experts (MoE), each sample in different omics adaptively determines the neighborhood ranges and architectures for information aggregation, while blocking unsuitable sub-GNNs. MMoG treats the complex multi-omics analysis as a multi-view learning problem, and essentially decomposes it into multiple sub-problems, allowing each omics/view to solve intersecting yet unique sub-problem groups. Additionally, we introduce mutual information-driven orthogonal loss and balancing loss to avoid view collapse. Extensive experiments on multi-omics data across multiple cancer types highlight MMoG's superiority.