Variation in gene copy number can alter gene expression and influence downstream phenotypes; thus copy-number variation (CNV) provides a route for rapid evolution if the benefits outweigh the cost. We recently showed that genetic background significantly influences how yeast cells respond to gene over-expression (OE), revealing that the fitness costs of CNV can vary substantially with genetic background in a common-garden environment. But the interplay between CNV tolerance and environment remains unexplored on a genomic scale. Here we measured the tolerance to gene OE in four genetically distinctSaccharomyces cerevisiaestrains grown under sodium chloride (NaCl) stress. OE genes that are commonly deleterious during NaCl stress recapitulated those commonly deleterious under standard conditions. However, NaCl stress uncovered novel differences in strain responses to gene OE. West African strain NCYC3290 and North American oak isolate YPS128 are more sensitive to NaCl stress than vineyard BC187 and laboratory strain BY4743. Consistently, NCYC3290 and YPS128 showed the greatest sensitivities to gene OE. Although most genes were deleterious, hundreds were beneficial when overexpressed – remarkably, most of these effects were strain specific. Few beneficial genes were shared between the NaCl-sensitive isolates, implicating mechanistic differences behind their NaCl sensitivity. Transcriptomic analysis suggested underlying vulnerabilities and tolerances across strains, and pointed to natural CNV of a sodium export pump that likely contributes to strain-specific responses to OE of other genes. Our results reveal extensive strain-by-environment interaction in the response to gene CNV, raising important implications for the accessibility of CNV-dependent evolutionary routes under times of stress.