Over the past 3 years, increased rates of mortgage foreclosures in the U.S. have resulted in widespread bankruptcies of financial institutions and massive losses of consumer wealth. The effects have been especially pronounced in economically vulnerable regions. In response, municipalities and community-based organizations provide a variety of services to mitigate the effects of foreclosures. Purchases of foreclosed properties represent a particularly attractive strategy because they have the potential to minimize blight, reduce unanticipated housing mobility, and to provide affordable homeownership opportunities. Since the cost of such purchases far exceeds the resources available in most urban centers, not-for-profit managers must solve the following decision problem: What subset of a large number of available foreclosed properties should be acquired for neighborhood stabilization and revitalization? In this paper, we present an extension of the multi-objective nonlinear knapsack problem to generate alternative portfolios of foreclosed multifamily rental properties to jointly optimize social benefits, social costs and equity. We apply our model to the Massachusetts city of Lowell, which has faced sharp increases in foreclosures since 2006. A subset of available Pareto-optimal solutions displays policy-relevant variation in decision space and objective space. We identify a promising compromise solution that places greatest emphasis on the goal of maximizing proximity of acquired units, and compare model results with strategies derived from heuristics inspired by real-life applications.