The study of the molecular mechanisms of stress appraisal on farmed fish is paramount to ensuring a sustainable aquaculture. Stress exposure can either culminate in the organism’s adaptation or aggravate into a metabolic shutdown, characterized by irreversible cellular damage and deleterious effects on fish performance, welfare, and survival. Multiomics can improve our understanding of the complex stressed phenotype in fish and the molecular mediators that regulate the underlying processes of the molecular stress response. We profiled the stress proteome and metabolome of Sparus aurata responding to different challenges common to aquaculture production, characterizing the disturbed pathways in the fish liver, i.e., the central organ in mounting the stress response. Label-free shotgun proteomics and untargeted metabolomics analyses identified 1738 proteins and 120 metabolites, separately. Mass spectrometry data have been made fully accessible via ProteomeXchange, with the identifier PXD036392, and via MetaboLights, with the identifier MTBLS5940. Integrative multivariate statistical analysis, performed with data integration analysis for biomarker discovery using latent components (DIABLO), depicted the 10 most-relevant features. Functional analysis of these selected features revealed an intricate network of regulatory components, modulating different signaling pathways related to cellular stress, e.g., the mTORC1 pathway, the unfolded protein response, endocytosis, and autophagy to different extents according to the stress nature. These results shed light on the dynamics and extent of this species’ metabolic reprogramming under chronic stress, supporting future studies on stress markers’ discovery and fish welfare research.