Many drug candidates fail in clinical trials due to an incomplete understanding of how small-molecule perturbations affect cell phenotype. Cellular responses can be non-intuitive due to systems-level properties such as redundant pathways caused by co-activation of multiple receptor tyrosine kinases. We therefore created a scalable algorithm, DIONESUS, based on partial least squares regression with variable selection to reconstruct a cellular signaling network in a human carcinoma cell line driven by EGFR overexpression. We perturbed the cells with 26 diverse growth factors and/or small molecules chosen to activate or inhibit specific subsets of receptor tyrosine kinases. We then quantified the abundance of 60 phosphosites at four time points using a modified microwestern array, a high-confidence assay of protein abundance and modification. DIONESUS, after being validated using three in silico networks, was applied to connect perturbations, phosphorylation, and cell phenotype from the high-confidence, microwestern dataset. We identified enhancement of STAT1 activity as a potential strategy to treat EGFR-hyperactive cancers and PTEN as a target of the antioxidant, n-acetylcysteine. Quantification of the relationship between drug dosage and cell viability in a panel of triple-negative breast cancer cell lines validated proposed therapeutic strategies.