The evolution toward sixth-generation (6G) wireless networks is driving larger antenna arrays and highly directional multi-beam transmission, making accurate knowledge of beam-dependent spatial coverage important for beam management and environment-aware network operation. Radio maps (RMs) provide such a representation, yet conventional RM prediction assumes omnidirectional or transmitter-level radiation. In beamformed multiple-input multiple-output (MIMO) systems, one propagation scene instead gives rise to many configuration-dependent beam radio maps (BeamRMs), creating challenges in beam representation and generalization. Existing methods either condition prediction on beam descriptors or use beam maps as auxiliary inputs to generic architectures. We propose BeamRMX, which, to the best of our knowledge, is the first dedicated framework to treat the spatial radiation pattern as the primary BeamRM query and learn how scene geometry transforms it into the received power field. XBase learns multiscale interactions between the radiation query and scene geometry, while an optional Evidence Adapter uses a few cross-configuration BeamRMs from the same scene. Matched-domain and zero-shot experiments show consistent gains over deterministic and diffusion baselines, including mean absolute error reductions of 26.1\% on unseen scenes and 47.8\% on an unseen configuration. Cross-configuration evidence further improves reconstruction and intra-sector beam refinement.

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