The best measure to limit spread of contagious diseases caused by influenza A viruses (IAVs) is annual vaccination. The growing global demand for low-cost vaccines requires the establishment of high-yield production processes. One possible option to address this challenge is the engineering of novel vaccine producer cell lines by manipulating gene expression of host cell factors relevant for virus replication. To support detailed characterization of engineered cell lines, we fitted an ordinary differential equation (ODE)-based model of intracellular IAV replication previously established by our group to experimental data obtained from infection studies in human A549 cells. Model predictions indicate that steps of viral RNA synthesis, their regulation and particle assembly and virus budding are promising targets for cell line engineering. The importance of these steps was confirmed in four of five single gene overexpression cell lines (SGOs) that showed small, but reproducible changes in early dynamics of RNA synthesis and virus release. Model-based analysis suggests, however, that overexpression of the selected host cell factors negatively influences specific RNA synthesis rates. Still, virus yield was rescued by an increase in the virus release rate. Based on parameter estimations obtained for SGOs, we predicted that there is a potential benefit associated with overexpressing multiple host cell genes in one cell line, which was validated experimentally. Overall, this model-based study on IAV replication in engineered cell lines provides a step forward in the dynamic and quantitative characterization of IAV-host cell interactions. Furthermore, it suggests targets for gene editing and indicates that overexpression of multiple host cell factors may be beneficial for the design of novel producer cell lines.