Multi-vector visual document retrieval models encode pages into hundreds of patch-level embeddings, enabling fine-grained interaction but incurring substantial storage overhead. Existing train-free compression approaches rely on token pruning or heuristic merging, which often fail to preserve the broad semantic coverage of the original representations under constrained budgets. To address this, we propose CovMerge, a geometry-aware, train-free index compression framework that formulates token reduction as a budgeted semantic coverage problem on the unit hypersphere. Given frozen patch embeddings, CovMerge applies Farthest Point Sampling (FPS) for coverage-aware prototype initialization, followed by spherical K-Means refinement aligned with MaxSim retrieval. The primary variant, Global Coverage, operates directly on all page patches without external dependencies, providing the strongest simplicity–efficiency trade-off. An optional Regional Coverage extension leverages document layout structure to guide prototype allocation, offering additional gains on layout-sensitive documents when reliable detection is available. Operating purely as post-processing without retraining, CovMerge supports flexible deployment budgets. On the ViDoRe V1 benchmark, CovMerge retains up to 98.1% and 98.6% of the original nDCG@5 for ColPali and ColQwen2, respectively, while using only 10% of the original storage, establishing a new state-of-the-art for storage-efficient multimodal retrieval.