We have developed a Pitzer model in the Na-K-Ca-Mg-Cl-SO4 system valid from 298.15 to <200 K up to saturated salt concentrations, which builds upon our previous low temperature model in the Na-K-Ca-Mg-Cl system. This model includes new experimental heat capacities in Na2SO4, K2SO4 and MgSO4 solutions measured using differential scanning calorimetry, as well as comprehensive heat capacities of crystalline phases, enthalpies of solution, activity coefficients, and solubilities from literature sources. The model improves over previous sulfate models because it accurately represents the thermodynamic properties of MgSO4 and its mixtures and more accurately represents gypsum and anhydrite equilibria in mixed salt solutions, in addition to accurate representations of many other salt systems. The model also includes temperature-dependent parameters for a number of new phases, such as variably hydrated Mg-sulfates, Na-sulfates, and polyhalite. This model is applicable to Cl-SO4-rich brines on Earth that typically evolve during evaporative or freezing modification of seawater, as well as Cl-SO4-rich planetary solutions.