This paper proposes TASER (Table Agents for Schema-guided Extraction and Recommendation), an agent-based system for extracting unstructured, multi-page table data from real-world financial documents. TASER transforms unstructured tables into regularized, schema-compliant output by utilizing agents that perform table detection, classification, extraction, and schema modification suggestions. Specifically, TASER incorporates schema improvements through continuous learning, emphasizes the effectiveness of large-scale batch learning, and achieves 10.1% performance improvement over existing models such as Table Transformer. Furthermore, we present a novel financial table dataset, TASERTab, which comprises 22,584 pages (28,150,449 tokens), 3,213 tables, and a total of $731,685,511,687 worth of asset data.