A generalized case-control (GCC) study, like the standard case-control study, leverages outcome-dependent sampling (ODS), but extends to non-binary response distributions. We develop a novel unifying approach for analyzing GCC study data using the recently developed semiparametric generalized linear model (GLM), which is substantially more robust to model misspecification than existing approaches based on parametric GLMs. For valid estimation and inference, we use a conditional likelihood to acknowledge the biased sampling design. We first describe analysis procedures under the Bernoulli sampling scheme, which selects each individual independently of others, and we show possible efficiency gains from GCC studies over equal probability sampling designs. Since independent sampling renders the ODS sample size random, we also extend our approach to accommodate analysis under fixed sample size GCC designs. We demonstrate the superiority of our approach over existing ones through extensive simulation studies and an application to the AHEAD study, which motives our research. The proposed approach yields a simple yet versatile ``plug-and-play'' solution for handling ODS.