Classical multiple instance learning (MIL) methods are often based on the identical and independent distributed assumption between instances, hence neglecting the potentially rich contextual information beyond individual entities. On the other hand, Transformers with global self-attention modules have been proposed to model the interdependencies among all instances. However, in this paper we question: Is global relation modeling using self-attention necessary, or can we appropriately restrict self-attention calculations to local regimes in large-scale whole slide images (WSIs)? We propose a general-purpose local attention graph-based Transformer for MIL (LA-MIL), introducing an inductive bias by explicitly contextualizing instances in adaptive local regimes of arbitrary size. Additionally, an efficiently adapted loss function enables our approach to learn expressive WSI embeddings for the joint analysis of multiple biomarkers. We demonstrate that LA-MIL achieves state-of-the-art results in mutation prediction for gastrointestinal cancer, outperforming existing models on important biomarkers such as microsatellite instability for colorectal cancer. This suggests that local self-attention sufficiently models dependencies on par with global modules. Our implementation will be published.