Humans and animals show remarkable flexibility in adjusting their behaviour when their goals, or rewards in the environment change. While such flexibility is a hallmark of intelligent behaviour, these multi-task scenarios remain an important challenge for machine learning algorithms and neurobiological models alike. We investigated two approaches that could enable this flexibility: factorized representations, which abstract away general aspects of a task from those prone to change, and nonparametric, memory-based approaches, which can provide a principled way of using similarity to past experiences to guide current behaviour. In particular, we combine the successor representation (SR), that factors the value of actions into expected outcomes and corresponding rewards, with evaluating task similarity through clustering the space of rewards. The proposed algorithm inverts a generative model over tasks, and dynamically samples from a flexible number of distinct SR maps while accumulating evidence about the current task context through amortized inference. It improves SR's transfer capabilities and outperforms competing algorithms and baselines in settings with both known and unsignalled rewards changes. Further, as a neurobiological model of spatial coding in the hippocampus, it explains important signatures of this representation, such as the "flickering" behaviour of hippocampal maps, and trajectory-dependent place cells (so-called splitter cells) and their dynamics. We thus provide a novel algorithmic approach for multi-task learning, as well as a common normative framework that links together these different characteristics of the brain's spatial representation.