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tokens: observations presented in Prochaska et al. ( 2017 ; hereafter P17 ). These data were previously analyzed using PIE models, which, as stated, are usually able to reproduce the low and intermediate ions but have trouble matching O vi (Lehner et al. 2013 ) without invoking very-low densities (Stern et al. 2016 ). The structure of this work is as follows. In Section 2 we discuss the observational data, and in Section 3 we give a brief description of MAIHEM as well as the MCMC code used to conduct our analysis. In Section 4 we show the main results of our analysis, followed by a discussion in Section 5 . 2. Data The data used for this analysis are a compilation of absorption-line systems probing the CGM of low-redshift galaxies from the COS–Halos survey. Specifically, we model the observations presented in P17 , which were previously analyzed using PIE models. These data consist of several ions for multiple absorbers along quasar sightlines that probe M ⊙ galaxies out to an impact parameter b ≈ 150 kpc (Tumlinson et al. 2013 ). The reader is encouraged to refer to previous work by the COS–Halos survey for additional details on the data collection and processing. Here, we study the same COS–Halos sightlines that were analyzed in P17 , for a total of 44 low-redshift ( z ≲ 0.5) systems. These sightlines exhibit absorption from a mixture of ionization states that include C ii , C iii , Fe ii , Fe iii , Mg ii , N ii , O i , O vi , Si ii , Si iii , Si iv , and S iii . As we now have the ability to model a multiphase medium, we also include Si iv and O vi , the column density for which were not incorporated into the analysis of P17 . We apply the MCMC analysis to the entire sample, finding, however, that only 32/44 systems converge on solutions with the MAIHEM model. Systems that are unable to find solutions have either all upper or lower limits, or only have accurate column density measurements for a single ion. When drawing comparisons with P17 , we thus limit our sample to only include the 32 systems with a converged solution. 3. Methods 3.1. MAIHEM Models We use the MAIHEM code to model ionic fractions in an isotropic turbulent medium. This cooling and chemistry package is a modified version of the open-source hydrodynamics code FLASH (Version 4.4) (Fryxell et al. 2000 ), which explicitly tracks the reaction network of 65 ions, including: hydrogen (H i and H ii ), helium (He i –He iii ), carbon (C i –C vi ), nitrogen (N i –N vii ), oxygen (O i –O viii ), neon (Ne i –Ne x ), sodium (Na i –Na iii ), magnesium (Mg i –Mg iv ), silicon (Si i –Si vi ), sulfur (S i –S v ), calcium (Ca i –Ca v ), iron (Fe i –Fe v ), and electrons from an initial non-equilibrium state to a steady state. Modifications for solving the hydrodynamic equations include using an unsplit solver based on Lee ( 2013 ), as well as a hybrid Riemann solver that utilizes the Harten Lax and van Leer solver (Einfeldt et al. 1991 ) to ensure stability in regions of strong shocks, and