Mercury is unique among the terrestrial planets for its relatively low mass (3.302 × 10²³ kg) and high average density (5.427 g cm⁻³) that together imply an unusual iron-rich bulk composition and thus provide an important constraint on planet formation and evolution and on compositional variations between the planets. In light of the recent discovery of a partially or fully molten core of Mercury, we model plausible interior density structures of Mercury using layered cores and the elastic properties of molten core materials. We present constraints on Mercury's decompressed density, composition, and interior structure, including elucidation of assumptions and methodology. We demonstrate the importance of molten and/or layered cores to accurately model Mercury's interior and to correctly interpret anticipated spacecraft geophysical observations. The core radius and core mass fraction will be tightly constrained by Earth-based radar and anticipated spacecraft tracking observations, but the bulk core sulfur content and extent of the molten core are less well constrained. Finally, we discuss the implications of incorporating molten materials in modeled density structures on the hypotheses of Mercury's iron enrichment and on anticipated spacecraft results.