Quadrupeds can generate various motor behaviors with the muscle synergies activated by the central nervous system. However, versatile locomotion for quadruped robots remains challenging due to the complexity of the high-dimensional limb dynamics with many physical constraints. Current approaches typically apply a dedicated policy or controller for each motor behavior, which requires the optimization of a large number of parameters and is not bionically sound. Inspired by the CNS and the muscle synergies of quadruped animals, we propose a Generalist Agent Learning Architecture (GALA) to learn diverse motor behaviors simultaneously with a single policy network for quadruped locomotion. GALA significantly decreases the number of trainable parameters while producing appropriate motor behaviors by simply reactivating the generalist policy based on different sensory feedback and commands at run time. We experimentally analyze and demonstrate the versatile locomotion delivered by GALA on both simulated and real quadruped robots in various environments. The code is available at https://github.com/vsislab/GALA.