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In test-based genetic programming (GP), the evolution is driven by program-test interactions that are naturally multidimensional. Previous works applied dimension reductions to these interaction matrices to form “derived objectives” that guide evolutionary multiobjective optimization (EMO). In this work, we consider tests as separate optimization targets as an alternative to reducing the interaction dimensionality. We compare methods based on different Pareto-front sampling strategies and propose a coevolutionary approach driven by a selection method based on extracting the underlying game structure from the interactions. This structure is a multidimensional coordinate system that maintains domination relations between programs along the axes and facilitates better sampling for breeding. Experimental results in discrete value domains demonstrate that the proposed methods have, in many cases, better performance on benchmarks than methods based on fitness aggregation, including dimensionality reduction.