Premature termination codon (PTC) mutations account for approximately 10% of pathogenic variants in monogenic diseases. Stimulation of translational readthrough, also known as stop codon suppression, using translational readthrough-inducing drugs (TRIDs) may serve as a possible therapeutic strategy for the treatment of genetic PTC diseases. One important parameter governing readthrough is the stop codon context (SCC)—the stop codon itself and the nucleotides in the vicinity of the stop codon on the mRNA. However, the quantitative influence of the SCC on treatment outcome and on appropriate drug concentrations are largely unknown. Here, we analyze the readthrough-stimulatory effect of various readthrough-inducing drugs on the SCCs of five common premature termination codon mutations of PEX5 in a sensitive dual reporter system. Mutations in PEX5, encoding the peroxisomal targeting signal 1 receptor, can cause peroxisomal biogenesis disorders of the Zellweger spectrum. We show that the stop context has a strong influence on the levels of readthrough stimulation and impacts the choice of the most effective drug and its concentration. These results highlight potential advantages and the personalized medicine nature of an SCC-based strategy in the therapy of rare diseases.