Ad-hoc systems are socio-technical systems emerging in response to dynamic problematic situations. These systems form when situation systems interact with respondent systems organized by human agents using elements available in the situation and assets brought in from outside the situation. The immediacy of formation, fast evolution, and short lifecycles of ad-hoc systems intertwine design, implementation, and operation activities in complex ways not addressed by current approaches to Systems Engineering focusing on more sedate environments. The proposed framework presents a language for classifying fundamental building blocks of ad-hoc systems – single-agent intervention, staging, readiness, and development systems. Further classification according to the physical location of agents and assets relative to situations generates 16 system classes on the 4x4 matrix of Ad-hoc Systems Gameboard, which is a helpful tool for managing the evolution of system portfolios. Combining the Gameboard with mapping the systems onto the PSI matrix reveals additional relationships and evolution patterns, opening up promising directions to address the challenge of designing, planning, and implementing interventions in complex situations.