Whole Slide Images (WSIs) are critical for various clinical applications, including histopathological analysis. However, current deep learning approaches in this field predominantly focus on individual tumor types, limiting model generalization and scalability. This relatively narrow focus ultimately stems from the inherent heterogeneity in histopathology and the diverse morphological and molecular characteristics of different tumors. To this end, we propose a novel approach for multi-cohort WSI analysis, designed to leverage the diversity of different tumor types. We introduce a Cohort-Aware Attention module, enabling the capture of both shared and tumor-specific pathological patterns, enhancing cross-tumor generalization. Furthermore, we construct an adversarial cohort regularization mechanism to minimize cohort-specific biases through mutual information minimization. Additionally, we develop a hierarchical sample balancing strategy to mitigate cohort imbalances and promote unbiased learning. Together, these form a cohesive framework for unbiased multi-cohort WSI analysis. Extensive experiments on a uniquely constructed multi-cancer dataset demonstrate significant improvements in generalization, providing a scalable solution for WSI classification across diverse cancer types. Our code for the experiments is publicly available at <link>.