Every protein progresses through a natural lifecycle from birth to maturation to death; this process is coordinated by the protein homeostasis system. Environmental or physiological conditions trigger pathways that maintain the homeostasis of the proteome. An open question is how these pathways are modulated to respond to the many stresses that an organism encounters during its lifetime. To address this question, we tested how the fitness landscape changes in response to environmental and genetic perturbations using directed and massively parallel transposon mutagenesis in . We developed a general computational pipeline for the analysis of gene-by-environment interactions in transposon mutagenesis experiments. This pipeline uses a combination of general linear models, statistical knockoffs, and a nonparametric Bayesian statistical model to identify essential genetic network components that are shared across environmental perturbations. This analysis allows us to quantify the similarity of proteotoxic environmental perturbations from the perspective of the fitness landscape. We find that essential genes vary more by genetic background than by environmental conditions, with limited overlap among mutant strains targeting different facets of the protein homeostasis system. We also identified 146 unique fitness determinants across different strains, with 19 genes common to at least two strains, showing varying resilience to proteotoxic stresses. Experiments exposing cells to a combination of genetic perturbations and dual environmental stressors show that perturbations that are quantitatively dissimilar from the perspective of the fitness landscape are likely to have a synergistic effect on the growth defect.