Neuronal ensembles encoding a specific memory have been shown to be distributed across multiple brain regions. However, the computational principles behind the distributed nature of such memory engrams are unknown. Here we propose that distributed engrams support functional flexibility and versatility. We investigated whether distributed engrams can differentially regulate memory discrimination and generalization, opposing and complementary computations that must be balanced for adaptive memory-guided behavior. For instance, while animals need to discriminate between threat-predictive and neutral stimuli, they also need to generalize threat-predictive cues to novel stimuli with shared features. By combining brain state-dependent and brain region-specific synaptic plasticity, our multi-region spiking neural network model can capture the emergence of functionally-connected and synaptically-coupled distributed engrams in line with experimental findings. Critically, our model generated two testable predictions. First, it predicted that while engrams in multiple brain regions promote memory generalization following initial encoding, a subset of regions subsequently switch to memory discrimination. Second, our model predicted that engrams in monosynaptically-connected brain regions are dynamic, allowing neurons to drop into and out of engrams in each region. Together, our results suggest that distributed engrams collectively form a flexible and versatile unified neural representation that: i) supports switching from memory generalization to discrimination for behavioral memory expression as observed experimentally, and ii) enables parallel memory generalization and discrimination at the neural level in distinct brain regions. Thus, our work proposes a testable theory that uncovers functional flexibility and versatility as computational principles underlying the distributed organization of memory.