Respiratory viral infections are a leading global cause of disease with multiple viruses detected in 20–30% of cases, and several viruses simultaneously circulating. Some infections with unique viral copathogens result in reduced pathogenicity, while other viral pairings can worsen disease. The mechanisms driving these dichotomous outcomes are likely variable and have only begun to be examined in the laboratory and clinic. To better understand viral–viral coinfections and predict potential mechanisms that result in distinct disease outcomes, we first systematically fit mathematical models to viral load data from ferrets infected with respiratory syncytial virus (RSV), followed by influenza A virus (IAV) after 3 days. The results suggest that IAV reduced the rate of RSV production, while RSV reduced the rate of IAV infected cell clearance. We then explored the realm of possible dynamics for scenarios that had not been examined experimentally, including a different infection order, coinfection timing, interaction mechanisms, and viral pairings. IAV coinfection with rhinovirus (RV) or SARS-CoV-2 (CoV2) was examined by using human viral load data from single infections together with murine weight-loss data from IAV-RV, RV-IAV, and IAV-CoV2 coinfections to guide the interpretation of the model results. Similar to the results with RSV-IAV coinfection, this analysis shows that the increased disease severity observed during murine IAV-RV or IAV-CoV2 coinfection was likely due to the slower clearance of IAV-infected cells by the other viruses. The improved outcome when IAV followed RV, on the other hand, could be replicated when the rate of RV infected cell clearance was reduced by IAV. Simulating viral–viral coinfections in this way provides new insights about how viral–viral interactions can regulate disease severity during coinfection and yields testable hypotheses ripe for experimental evaluation.