Selection in novel environments can lead to a coordinated evolutionary response across a suite of characters. Environmental conditions can also potentially induce changes in the genetic architecture of complex traits, which in turn could alter the pattern of the multivariate response to selection. We describe a factorial selection experiment using the nematode Caenorhabditis remanei in which two different stress-related phenotypes (heat and oxidative stress resistance) were selected under three different environmental conditions. The pattern of covariation in the evolutionary response between phenotypes or across environments differed depending on the environment in which selection occurred, including asymmetrical responses to selection in some cases. These results indicate that variation in pleiotropy across the stress response network is highly sensitive to the external environment. Our findings highlight the complexity of the interaction between genes and environment that influences the ability of organisms to acclimate to novel environments. They also make clear the need to identify the underlying genetic basis of genetic correlations in order understand how patterns of pleiotropy are distributed across complex genetic networks.