We propose a two-stage methodology to support decision-making for large/complex multiobjective optimization problems (MOPs) with a decomposable structure, regardless of whether the MOP, due to its size, is solvable in its entirety. During the first stage, the MOP is decomposed into a collection of multiobjective subproblems each of which have fewer objectives than the original MOP. The second stage utilizes the new notion of subproblem tradeoffs, which allow decision makers (DMs) to coordinate the subproblems and select a Pareto efficient solution satisfying their overall and subproblem-level preferences while maintaining a holistic view of the large/complex MOP. We then present three decision-making procedures which capitalize on the insights provided by subproblem tradeoffs. Finally, we demonstrate the effectiveness of the methodology on an example inspired by disaster relief.