This paper explores novel approaches under the design inquiry paradigm that promise to help organizations better understand and solve socio-technical dilemmas. Design inquiry is contrasted with scientific inquiry (Section 1). Section 2 presents a meso-scale model of models methodology for design inquiry that synthesizes systems science, agent modeling and simulation, knowledge management architectures, and domain theories and knowledge. The goal is to focus computational science on exploring underlying mechanisms (white box modeling) and to support reflective theorizing and discourse to explain social dilemmas and potential resolutions. Section 3 then describes an evolving agent modeling and simulation testbed while Section 4 offers two gameworld applications that implement this approach and that serve as an example of the new types of instruments useful for systems social science. The conclusions wrapup by reviewing lessons learned about 10 criteria that have guided this research.