Multi-image super-resolution (MISR) can achieve higher image quality than single-image super-resolution (SISR) by aggregating sub-pixel information from multiple spatially shifted frames. Among MISR tasks, burst super-resolution (BurstSR) has gained significant attention due to its wide range of applications. Recent methods have increasingly adopted Transformers over convolutional neural networks (CNNs) in super-resolution tasks, due to their superior ability to capture both local and global context. However, most existing approaches still rely on fixed and narrow attention windows that restrict the perception of features beyond the local field. This limitation hampers alignment and feature aggregation, both of which are crucial for high-quality super-resolution. To address these limitations, we propose a novel feature extractor that incorporates two newly designed attention mechanisms: overlapping cross-window attention and cross-frame attention, enabling more precise and efficient extraction of sub-pixel information across multiple frames. Furthermore, we introduce a Multi-scan State-Space Module with the cross-frame attention mechanism to enhance feature aggregation. Extensive experiments on both synthetic and real-world benchmarks demonstrate the superiority of our approach. Additional evaluations on ISO 12233 resolution test charts further confirm its enhanced super-resolution performance.