Pathological cardiomyocyte hypertrophy is a response to cardiac stress that typically leads to heart failure. Despite being a primary contributor to pathological cardiac remodelling, the therapeutic space that targets hypertrophy is limited. Here, we apply a network model to virtually screen for FDA-approved drugs that induce or suppress cardiomyocyte hypertrophy. A logic-based differential equation model of cardiomyocyte signalling was used to predict drugs that modulate hypertrophy. These predictions were validated against curated experiments from the prior literature. The actions of midostaurin were validated in new experiments using TGFβ- and noradrenaline (NE)-induced hypertrophy in neonatal rat cardiomyocytes. Model predictions were validated in 60 out of 70 independent experiments from the literature and identify 38 inhibitors of hypertrophy. We additionally predict that the efficacy of drugs that inhibit cardiomyocyte hypertrophy is often context dependent. We predicted that midostaurin inhibits cardiomyocyte hypertrophy induced by TGFβ, but not noradrenaline, exhibiting context dependence. We further validated this prediction by cellular experiments. Network analysis predicted critical roles for the PI3K and RAS pathways in the activity of celecoxib and midostaurin, respectively. We further investigated the polypharmacology and combinatorial pharmacology of drugs. Brigatinib and irbesartan in combination were predicted to synergistically inhibit cardiomyocyte hypertrophy. This study provides a well-validated platform for investigating the efficacy of drugs on cardiomyocyte hypertrophy and identifies midostaurin for consideration as an antihypertrophic drug.