The brain has a remarkable ability to maintain a flexible behavioral repertoire which must continuously expand to accommodate new knowledge, a form of ‘continual learning’. Unlike mainstream artificial networks, which require complex and computationally expensive systems to achieve similar versatility, biological brains efficiently generalize prior learning, making inferences to acquire new tasks and perform multiple tasks based on context. Despite being an ideal species for neural investigation, mice have typically been thought to exhibit limited cognitive capacity for such complex learning paradigms. To address this, we developed a scalable experimental platform where multiple co-housed mice live 24/7 in an automated home-cage and can individually access one, two, or four arenas to perform self-initiated decision-making tasks. This ‘Continual Learning Mouse Playground’ allows us to train mice on many tasks with minimal supervision. We developed a novel behavioral framework that organizes tasks along two axes: task structure (e.g., go/no-go, two-alternative forced choice) and auditory perceptual dimension (e.g., frequency, duration). We trained mice (n=8) to learn 8 tasks which took <40 days with high retention of prior tasks. Over the first six tasks, mice were exposed to all task structures and perceptual dimensions, but not each combination. We then tested mice on a combination they had never experienced. Strikingly, some mice exhibited the capacity for immediate compositional inference. A dynamic generalized linear model demonstrated that compositional learners exhibited high stimulus weights from the outset in Tasks 7 and 8 with little choice bias, unlike slower learners. Finally, we used a neural network model, featuring an 'ensembler' architecture, which recapitulated the learning trajectories of compositional learners by implementing efficient bidirectional transfer. Together, these results suggest that compositional inference in mice relies on higher-order representations of distinct task dimensions that can be flexibly recombined on demand.