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We present a stellar parameter catalog built to accompany the MaStar Stellar Library, which is a comprehensive collection of empirical, medium-resolution stellar spectra. We constructed this parameter catalog by using a multicomponent $χ^{2}$ fitting approach to match MaStar spectra to models generated by interpolating the ATLAS9-based BOSZ model spectra. The total $χ^{2}$ for a given model is defined as the sum of components constructed to characterize narrow-band features of observed spectra (e.g., absorption lines) and the broadband continuum shape separately. Extinction and systematics due to flux calibration were taken into account in the fitting. The $χ^{2}$ distribution for a given region of model space was sampled using a Markov Chain Monte Carlo (MCMC) algorithm, the data from which were then used to extract atmospheric parameter estimates ($T_{eff}$, log g, [Fe/H], and [$α$/Fe]), their corresponding uncertainties, and direct extinction measurements. Two methods were used to extract parameters and uncertainties: one that accepts the MCMC's prescribed minimum-$χ^{2}$ result, and one that uses Bayesian inference to compute a likelihood-weighted mean from the $χ^{2}$ distribution sampled by the MCMC. Results were evaluated for internal consistency using repeat observations where available and by comparing them with external data sets (e.g., APOGEE-2 and Gaia DR2). Our spectral-fitting exercise reveals possible deficiencies in current theoretical model spectra, illustrating the potential power of MaStar spectra for helping to improve the models. This paper represents an update to the parameters that were originally presented with SDSS-IV DR17. The MaStar parameter catalog containing our BestFit results is available on the SDSS-IV DR17 website as part of version 2 of the MaStar stellar parameter value-added catalog.