Most modern approaches to quadruped locomotion focus on using Deep Reinforcement Learning (DRL) to learn policies from scratch, in an end-to-end manner. Such methods often fail to scale, as every new problem or application requires time-consuming and iterative reward definition and tuning. We present Generalist Contact-Conditioned Policy (GeCCo) -- a low-level policy trained with Deep Reinforcement Learning that is capable of tracking arbitrary contact points on a quadruped robot. The strength of our approach is that it provides a general and modular low-level controller that can be reused for a wider range of high-level tasks, without the need to re-train new controllers from scratch. We demonstrate the scalability and robustness of our method by evaluating on a wide range of locomotion and manipulation tasks in a common framework and under a single generalist policy. These include a variety of gaits, traversing complex terrains (eg. stairs and slopes) as well as previously unseen stepping-stones and narrow beams, and interacting with objects (eg. pushing buttons, tracking trajectories). Our framework acquires new behaviors more efficiently, simply by combining a task-specific high-level contact planner and the pre-trained generalist policy. A supplementary video can be found at https://youtu.be/o8Dd44MkG2E.