Quinazoline derivatives constitute a large family of small-molecule inhibitors of tyrosine kinases. In the current study, the p53 protein reactivator CP-31398 was tested against a panel of kinases on the assumption that it was structurally similar to other active inhibitors. Although it was found to be active in the enzyme-based assay, this compound did not block the proliferation of cancer cells at a feasible concentration level. The styrylquinazoline was used to design new structures that might be potential multitarget inhibitors. Subsequently, a series of compounds was obtained and characterized. Their inhibitory activity in a panel of tyrosine kinases had an antiproliferative effect against several cancer cell lines that have different expression levels of those proteins. The mode of protein interaction was tested for the most active compound in docking experiments.