Abstract Prokaryotes are under nearly constant attack by viral pathogens. To protect against this threat of infection, bacteria and archaea have evolved a wide array of defense mechanisms, singly and in combination. While immune diversity in a single organism likely reduces the chance of pathogen evolutionary escape, it remains puzzling why many prokaryotes also have multiple, seemingly redundant, copies of the same type of immune system. Here, we focus on the highly flexible CRISPR adaptive immune system, which is present in multiple copies in a surprising 28% of the prokaryotic genomes in RefSeq. We use a comparative genomics approach looking across all prokaryotes to demonstrate that, on average, organisms are under selection to maintain more than one CRISPR array. We hypothesize that a tradeoff between memory span and learning speed could select for both “long-term memory” and “short-term memory” CRISPR arrays, and we go on to develop a mathematical model to show that such a tradeoff could, in theory, lead to selection for multiple arrays.