Interactive optimization leverages the strengths of optimization frameworks alongside the expertise of human users. Prior research in this area tends to either ask human users for the same type of information, or when varying information is requested, users must manually modify the optimization model directly. These limitations restrict the incorporation of wider human knowledge into the problem domain and demand a higher level of optimization expertise from the user. To address these challenges, we propose a new iterative interactive optimization framework that enables human users to answer multiple types of questions, with their input being transformed to create a higher fidelity stochastic multi-objective mixed integer linear programming model (SM-MILP). The goal of the framework is to arrive at an SM-MILP that can recommend design solutions satisfactory to the human designer. Our framework can ask the human user targeted questions to extract important information while reducing the solution’s performance uncertainty through a Conditional Value at Risk (CVaR) formulation. The conducted computational experiments on a supplier selection problem demonstrate that this iterative framework can reduce the reality gap while converging faster to the ground truth solution and reducing the confidence interval length.