Key Information Extraction (KIE) from visually rich documents is commonly approached as either fine-grained token classification or coarse-grained entity extraction. While token-level models capture spatial and visual cues, entity-level models better represent logical dependencies and align with real-world use cases.We introduce PM3-KIE, a probabilistic multi-task meta-model that incorporates both fine-grained and coarse-grained models. It serves as a lightweight reasoning layer that jointly predicts entities and all appearances in a document. PM3-KIE incorporates domain-specific schema constraints to enforce logical consistency and integrates large language models for semantic validation, thereby reducing extraction errors.Experiments on two public datasets, DeepForm and FARA, show that PM3-KIE outperforms three state-of-the-art models and a stacked ensemble, achieving a statistically significant 2% improvement in F1 score.