Precise maxillomandibular relationship reconstruction is fundamental in digital dentistry but is challenged by the lack of direct overlap between opposing arches. This paper presents MAGIC-OR (Multi-dimensional Alignment with Geometric Constraints for Occlusal Reconstruction), a framework integrating multi-dimensional intraoral scanning with geometric constraint optimization. Our method uses a dual-buccal scanning approach as a registration bridge, with an intelligent selection mechanism to mitigate occlusal asymmetry-induced scan quality challenges in clinical datasets. We also developed a geometry-constrained refinement algorithm that evaluates biomechanical parameters (centroid distance, contact density, normal alignment, gap distribution) to systematically eliminate model interpenetration and optimize occlusal stability. Validation on 49 clinical cases demonstrates that MAGIC-OR significantly advances maxillomandibular registration by effectively addressing the challenge of limited inter-arch overlap.