Clinical efficacy regularly requires the combination of drugs. For an early estimation of the clinical value of (potentially many) combinations of pharmacologic compounds during discovery, the observed combination effect is typically compared to that expected under a null model. Mechanistic accuracy of that null model is not aspired to; to the contrary, combinations that deviate favorably from the model (and thereby disprove its accuracy) are prioritized. Arguably the most popular null model is the Loewe Additivity model, which conceptually maps any assay under study to a (virtual) single-step enzymatic reaction. It is easy-to-interpret and requires no other information than the concentration-response curves of the individual compounds. However, the original Loewe model cannot accommodate concentration-response curves with different maximal responses and, by consequence, combinations of an agonist with a partial or inverse agonist. We propose an extension, named Biochemically Intuitive Generalized Loewe (BIGL), that can address different maximal responses, while preserving the biochemical underpinning and interpretability of the original Loewe model. In addition, we formulate statistical tests for detecting synergy and antagonism, which allow for detecting statistically significant greater/lesser observed combined effects than expected from the null model. Finally, we demonstrate the novel method through application to several publicly available datasets.