<p>Accurate reconstruction of the maxillomandibular relationship is essential for successful prosthetic rehabilitation in digital dentistry. Conventional registration techniques are severely constrained by the absence of direct overlap between the upper and lower dental arches and by their sensitivity to common clinical occlusal variations. In this paper, we introduce MAGIC-OR (Multi-dimensional Alignment with Geometric Intraoral Constraints for Occlusal Reconstruction), a framework that tightly couples multi-view intraoral scanning with geometric constraint optimization. The core of the method is a dual-buccal scanning strategy that exploits the buccal surfaces as a reliable registration bridge; an automatic selection mechanism identifies the optimal transformation among the bilateral scans, thereby coping effectively with occlusal asymmetry and unilateral data degradation. Building on this initial alignment, a geometry-constrained refinement engine with an enhanced safety metric (jointly penalizing penetration frequency, mean depth, and maximum depth) simultaneously evaluates biomechanical features-centroid distance, contact density, normal vector alignment, and gap distribution-to systematically suppress inter-arch penetration while promoting occlusal contact uniformity and stability. Comprehensive weight sensitivity analysis and ablation studies are conducted to quantify the contribution of each geometric constraint. Experiments on 155 clinical cases confirm that MAGIC-OR offers a notable advance in maxillomandibular registration, directly tackling the fundamental difficulty of limited inter-arch overlap through its geometric, dual-buccal optimization paradigm.</p>