Mechanistic trade-offs between traits under selection can shape and constrain evolutionary adaptation to environmental stressors. However, our knowledge of the quantitative and qualitative overlap in the molecular machinery among stress tolerance traits is highly restricted by the challenges of comparing and interpreting data between separate studies and laboratories, as well as to extrapolating between different levels of biological organization. We investigated the expression of the constitutive proteome (833 proteins) of 35 Drosophila melanogaster replicate populations artificially selected for increased resistance to six different environmental stressors. The evolved proteomes were significantly differentiated from replicated control lines. A targeted analysis of the constitutive proteomes revealed a regime-specific selection response among heat-shock proteins, which provides evidence that selection also adjusts the constitutive expression of these molecular chaperones. Although the selection response in some proteins was regime specific, the results were dominated by evidence for a “common stress response.” With the exception of high temperature survival, we found no evidence for negative correlations between environmental stress resistance traits, meaning that evolutionary adaptation is not constrained by mechanistic trade-offs in regulation of functional important proteins. Instead, standing genetic variation and genetic trade-offs outside regulatory domains likely constrain the evolutionary responses in natural populations.