Investors in international agricultural research seek sustainable agri-food technologies that can potentially serve multiple objectives, including economic growth, food security, and sustainable use of natural resources. We employ quantitative economic models to examine the potential multi-dimensional impacts of agricultural productivity gains in the Global South. These models take into account behavior responses to agricultural technological change, i.e., how productivity changes may affect decisions on what to produce, trade, and consume. We compare potential impacts of productivity growth in different commodities and regions and assess implications along several impact dimensions, including economic and income growth, the population at risk of hunger, adequacy of protein and micronutrients in human diets, land and water use, and greenhouse gas emissions. Potential impacts vary widely by commodity group and by region. These results reveal strengths and potential tradeoffs of different R&D spending allocations, and can help inform decision-making about an optimal R&D portfolio that takes into account the multiple objectives of agricultural investments.