We model the density structure of the outer several tens of kilometers of Io on the basis of the assumption that condensed volatiles, mainly SO2, exist at shallow depths in a mafic to ultramafic lithosphere, which has a finite porosity due to its accumulation as a mixture of pyroclastic and effusive volcanic deposits, which include condensed volatiles. The porosity decreases with increasing depth due to pressure-driven compaction and temperature-driven melting of the volatiles, and this controls the bulk density structure of the lithosphere. We also model the densities of ascending magmas as a function the types and amounts of volatiles that are available in their source regions. The relative densities of the accumulated volcanic deposits and of the magmas rising through them control whether the magmas will erupt at the surface or will stall to form intrusions which can grow into magma reservoirs. We find that the depths at which magma reservoirs may exist are strongly influenced by the void space fraction in surface deposits and only weakly controlled by the mass fraction of SO2 in the deposits and the mass fraction of SO2 in the magmas. Once nucleated, a reservoir has the potential to grow to a very large vertical extent (∼15 km total height) before the magma immediately beneath its roof is again buoyant relative to the surrounding rocks. The presence of large-volume reservoirs may explain the great extent of the larger lava flow fields seen on Io and the longevity of some eruptions. The presence of very soluble volatiles, such as water, in magmas would have virtually no effect on these findings because these volatiles would influence the densities of magmas only very near the surface (though they would, even in very small amounts, then have a dramatic effect on the explosivities of eruptions).