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The relationship between sequence design and the diversity of the resultant phases is therefore of interest. Here, we explore this question using the DNA nanostar system which permits the creation of multiphase condensate droplets through sequence engineering of the sticky end bonds that drive particle\u2013particle attraction. We explore the theoretical limits of nanostar phase diversity, then experimentally demonstrate the ability to create nine distinct, nonadhering nanostar phases that do not share components. We further study how different thermal histories affect the morphology and dynamics of such a highly diverse condensate system. We particularly show that a rapid temperature quench leads to the formation of a densely packed 2-D layer of droplets that is transiently stabilized by caging effects enabled by the phase diversity, leading to glassy dynamics such as slow coarsening and dynamic heterogeneity. 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