Large silicic ignimbrites commonly erupt from compositionally variable reservoirs. Although ignimbrite compositional architecture is often consistent with evacuation of a single zoned magma body, other examples are better interpreted as the products of amalgamation of multiple discrete subvolcanic melt-rich lenses. For example, multiple populations of pyroxene crystals and glass fragments within single ignimbrites from the central Snake River Plain (Idaho, USA) support the multibatch model. This presents a conundrum in terms of magma generation and storage; if the crystal-poor silicic magma batches are not generated nearly in situ in the upper crust, they must traverse, and reside within, a thermally hostile environment with large temperature gradients, resulting in low survivability in their shallow magmatic hearths. Ubiquitous crystal aggregates in central Snake River Plain rhyolites hint at another model. These aggregates contain the same plagioclase, pyroxene, and oxide mineral compositions as single phenocrysts of the same minerals in their host rocks, but they have significantly less silicic bulk compositions and lack quartz and sanidine, which occur as single phenocrysts in the deposits. These observations imply significant crystallization followed by melt extraction from mushy margins of the magma reservoirs. The extracted melt then pools and continues to evolve (crystallizing sanidine and quartz) while the melt-depleted walls and/or floors provide an increasingly rigid and refractory network segregating the crystal-poor batches of magma. Such hot refractory margins insulate the crystal-poor lenses, allowing (1) extended residence in the upper crust, and (2) preservation of chemical heterogeneities among batches. In contrast, systems that produce cumulates richer in low-temperature phases (quartz, K-feldspars, and/or biotite) can melt extensively upon recharge, leading to less segregation of eruptible melt pockets and the formation of gradationally zoned ignimbrites.