Partial Satisfaction or Over-subscription Planning problems arise in many real world applications. Applications in which the planning agent does not have enough resources to accomplish all of their given goals, requiring plans that satisfy only a subset of them. Solving such partial satisfaction planning (PSP) problems poses several challenges, from new models for handling plan quality to efficient heuristics for selecting the most beneficial goals. In this paper, we extend planning graph-based reachability heuristics with mutex analysis to overcome complex goal interactions in PSP problems. We start by describing one of the most general PSP problems, the PSP Net Benefit problem, where actions have execution costs and goals have utilities. Then, we present AltWlt, our heuristic approach augmented with a multiple goal set selection process and mutex analysis. Our empirical studies show that AltWlt is able to generate the most beneficial solutions, while incurring only a small fraction of the cost of other PSP approaches.