Storing memories of ongoing, everyday experiences requires a high degree of plasticity, but retaining these memories demands protection against changes induced by further activity and experience. Models in which memories are stored through switch-like transitions in synaptic efficacy are good at storing but bad at retaining memories if these transitions are likely, and they are poor at storage but good at retention if they are unlikely. We construct and study a model in which each synapse has a cascade of states with different levels of plasticity, connected by metaplastic transitions. This cascade model combines high levels of memory storage with long retention times and significantly outperforms alternative models. As a result, we suggest that memory storage requires synapses with multiple states exhibiting dynamics over a wide range of timescales, and we suggest experimental tests of this hypothesis.