We introduce MOSCATO: a new benchmark for predicting the evolving states of multiple objects through long procedural videos with multiple actions. While prior work in object state prediction has typically focused on a single object undergoing one or a few state changes, real-world tasks require tracking many objects whose states evolve over multiple actions. Given the high cost of gathering framewise object-state labels for many videos, we develop a weakly-supervised multiple object state prediction framework, which only uses action labels during training. Specifically, we propose a novel Pseudo-Label Acquisition (PLA) pipeline that integrates large language models, vision–language models, and action segment annotations to generate fine-grained, per-frame object-state pseudo-labels for training a Multiple Object State Prediction (MOSP) network. We further devise a State–Action Interaction (SAI) module that explicitly models the correlations between actions and object states, thereby improving MOSP. To facilitate comprehensive evaluation, we create the MOSCATO benchmark b y augmenting three egocentric video datasets with framewise object-state annotations. Experiments show that our multi-stage pseudo-labeling approach and SAI module significantly boost performance over zero-shot VLM baselines and naive extensions of existing methods, underscoring the importance of holistic action–state modeling for fine-grained procedural video understanding.