Solar wind charge exchange (SWCX) emission contaminates all astrophysical observations in X-rays regardless of the direction. This contamination is particularly problematic when measuring astrophysical plasma temperatures due to the similar spectral distribution of the two phenomena. Since its discovery, literature has distinguished between SWCX emission resulting from solar wind-neutral interactions within the Earth's magnetosphere, called magnetospheric SWCX, and similar interactions occurring more generally throughout the heliosphere, called heliospheric SWCX. Previous work demonstrated accurate modeling of the heliospheric SWCX contribution for astrophysical observations performed at low ecliptic latitude with HaloSat, a CubeSat X-ray mission of medium spectral resolution. Here, we apply this model to similarly orchestrated observations to measure the magnetospheric SWCX contribution separately from the heliospheric SWCX and the astrophysical background contributions. We describe our observational strategy, the heliospheric SWCX model used, and our spectral fitting methods. In particular, we report on four observations with lines of sight through the Earth's magnetospheric flank with total O VII line fluxes at least 3σ above that predicted by the heliospheric SWCX model and the astrophysical background, possibly indicative of magnetospheric SWCX. We then discuss the excess emission in comparison with available magnetospheric SWCX simulations requested through the Community Coordinated Modeling Center.