During viral infection, the numbers of virions infecting individual cells can vary significantly over time and space. The functional consequences of this variation in cellular multiplicity of infection (MOI) remain poorly understood. Here, we rigorously quantify the phenotypic consequences of cellular MOI during influenza A virus (IAV) infection over a single round of replication in terms of cell death rates, viral output kinetics, interferon and antiviral effector gene transcription, and superinfection potential. By statistically fitting mathematical models to our data, we precisely define specific functional forms that quantitatively describe the modulation of these phenotypes by MOI at the single cell level. To determine the generality of these functional forms, we compare two distinct cell lines (MDCK cells and A549 cells), both infected with the H1N1 strain A/Puerto Rico/8/1934 (PR8). We find that a model assuming that infected cell death rates are independent of cellular MOI best fits the experimental data in both cell lines. We further observe that a model in which the rate and efficiency of virus production increase with cellular co-infection best fits our observations in MDCK cells, but not in A549 cells. In A549 cells, we also find that induction of type III interferon, but not type I interferon, is highly dependent on cellular MOI, especially at early timepoints. This finding identifies a role for cellular co-infection in shaping the innate immune response to IAV infection. Finally, we show that higher cellular MOI is associated with more potent superinfection exclusion, thus limiting the total number of virions capable of infecting a cell. Overall, this study suggests that the extent of cellular co-infection by influenza viruses may be a critical determinant of both viral production kinetics and cellular infection outcomes in a host cell type-dependent manner.