We present a new analysis of the KELT-24 system, comprising a well-aligned hot Jupiter, KELT-24 b, and a bright (V=8.3), nearby (d=96.9pc) F-type host star. KELT-24 b was independently discovered by two groups in 2019, with each reporting best-fit stellar parameters that were notably inconsistent. Here, we present three independent analyses of the KELT-24 system, each incorporating a broad range of photometric and spectroscopic data, including eight sectors of Transiting Exoplanet Survey Satellite (TESS) photometry and more than 200 new radial velocities (RVs) from the MINiature Exoplanet Radial Velocity Array. Two of these analyses use KELT-24's observed spectral energy distribution (SED) through a direct comparison to stellar evolutionary models, while our third analysis assumes an unknown additional body contributing to the observed broadband photometry and excludes the SED. Ultimately, we find that the models that include the SED are a poor fit to the available data, so we adopt the system parameters derived without it. We also highlight a single transit-like event observed by TESS, deemed likely to be an eclipsing binary bound to KELT-24, that will require follow-up observations to confirm. We discuss the potential of these additional bodies in the KELT-24 system as a possible explanation for the discrepancies between the results of the different modeling approaches, and explore the system for longer-period planets that may be weakly evident in the RV observations. The comprehensive investigations that we present not only increase the fidelity of our understanding of the KELT-24 system but also serve as a blueprint for future stellar modeling in global analyses of exoplanet systems.