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The prefrontal cortex encodes and stores numerous, often disparate, schemas and flexibly switches between them. Recent research on artificial neural networks trained by reinforcement learning has made it possible to model fundamental processes underlying schema encoding and storage. Yet how the brain is able to create new schemas while preserving and utilizing old schemas remains unclear. Here we propose a simple neural network framework that incorporates hierarchical gating to model the prefrontal cortex’s ability to flexibly encode and use multiple disparate schemas. We show how gating naturally leads to transfer learning and robust memory savings. We then show how neuropsychological impairments observed in patients with prefrontal damage are mimicked by lesions of our network. Our architecture, which we call DynaMoE, provides a fundamental framework for how the prefrontal cortex may handle the abundance of schemas necessary to navigate the real world.