Recent advancements in large-scale offline training have demonstrated the potential of generalist policy learning for complex robotic tasks. However, applying these principles to legged locomotion remains a challenge due to continuous dynamics and the need for real-time adaptation across diverse terrains and robot morphologies. In this work, we propose GRoQ-LoCO, a scalable, attention-based framework that learns a single generalist locomotion policy across multiple quadruped robots and terrains, relying solely on offline datasets. Our approach leverages expert demonstrations from two distinct locomotion behaviors - stair traversal (non-periodic gaits) and flat terrain traversal (periodic gaits) - collected across multiple quadruped robots, to train a generalist model that enables behavior fusion. Crucially, our framework operates solely on proprioceptive data from all robots without incorporating any robot-specific encodings. The policy is directly deployable on an Intel i7 nuc, producing low-latency control outputs without any test-time optimization. Our extensive experiments demonstrate zero-shot transfer across highly diverse quadruped robots and terrains, including hardware deployment on the Unitree Go1, a commercially available 12kg robot. Notably, we evaluate challenging cross-robot training setups where different locomotion skills are unevenly distributed across robots, yet observe successful transfer of both flat walking and stair traversal behaviors to all robots at test time. We also show preliminary walking on Stoch 5, a 70kg quadruped, on flat and outdoor terrains without requiring any fine tuning. These results demonstrate the potential of offline, data-driven learning to generalize locomotion across diverse quadruped morphologies and behaviors.