Recovering the relative 6-DoF pose between two image groups underlies cross-sequence relocalization and multi-camera rig odometry. Each group carries known intra-group geometry from visual odometry or rig calibration, and pretrained multi-view backbones already fuse such geometry into visual features. Yet current models treat all views as an unstructured set, leaving cross-group reasoning as the missing piece. We introduce \ours{}, which keeps the foundation model entirely frozen and adds three lightweight trainable modules to bridge the two groups: a perceiver resampler, a cross-group bridge with merged self-attention, and a multi-frame pose head. The trainable footprint totals about 32M parameters, under 6\% of the full model, and is supervised only by relative poses. Across four datasets that span indoor and outdoor simulation, real-world cross-season capture, and zero-shot sim-to-real transfer, \ours{} attains state-of-the-art accuracy on both tasks, while every baseline is retrained with its full original supervision. Code is available at https://github.com/WeiYuFei0217/G2G.