Martian primary compositions, i.e., magmas that did not experience fractionation and/or contamination after extraction from the mantle, occur as a subset of Martian meteorites and a few lavas analyzed on the planet's surface by rovers. Eruptions of primary magmas are rare on Earth and presumably on Mars. Previous studies of fractional crystallization of Martian primary magmas have been conducted under isobaric conditions, simulating idealized crystallization in magma chambers. Polybaric fractionation, which occurs during magma ascent, has not been investigated in detail for Martian magmas. Using the MELTS algorithm and the pMELTS revision, we present comprehensive isobaric and polybaric thermodynamic calculations of the fractional crystallization of four primary or parental Martian magmas (Humphrey, Fastball, Y-980459 shergottite, and nakhlite parental melts) using various pressure-temperature paths, oxygen fugacities, and water contents to constrain how these magmas might evolve. We then examine whether known Martian alkaline rock compositions could have formed through fractional crystallization of these magmas under the simulated conditions. We find that isobaric and polybaric crystallization paths produce similar residual melt compositions, but given sufficient details, we may be able to distinguish between them. We calculate that Backstay (Gusev Crater) likely formed by fractionation of a primary magma under polybaric conditions, while Jake_M (Gale Crater) may have formed through melting of a metasomatized mantle, crustal assimilation, or fractional crystallization of an unknown primary magma. The best fits for the Backstay composition indicate that consideration of polybaric crystallization paths can help improve the quality of fit when simulating liquid lines of descent.