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Metazoan adaptation to global change relies on selection of standing genetic variation. Determining the extent to which this variation exists in natural populations, particularly for responses to simultaneous stressors, is essential to make accurate predictions for persistence in future conditions. Here, we identified the genetic variation enabling the copepod Acartia tonsa to adapt to experimental ocean warming, acidification, and combined ocean warming and acidification (OWA) over 25 generations of continual selection. Replicate populations showed a consistent polygenic response to each condition, targeting an array of adaptive mechanisms including cellular homeostasis, development, and stress response. We used a genome-wide covariance approach to partition the allelic changes into three categories: selection, drift and replicate-specific selection, and laboratory adaptation responses. The majority of allele frequency change in warming (57%) and OWA (63%) was driven by shared selection pressures across replicates, but this effect was weaker under acidification alone (20%). OWA and warming shared 37% of their response to selection but OWA and acidification shared just 1%, indicating that warming is the dominant driver of selection in OWA. Despite the dominance of warming, the interaction with acidification was still critical as the OWA selection response was highly synergistic with 47% of the allelic selection response unique from either individual treatment. These results disentangle how genomic targets of selection differ between single and multiple stressors and demonstrate the complexity that nonadditive multiple stressors will contribute to predictions of adaptation to complex environmental shifts caused by global change.