Current operational models of agonism and allosterism quantify ligand actions at receptors where agonist concentration-response relationships are nonhyperbolic by introduction of a transducer slope that relates receptor occupancy to response. However, for some receptors nonhyperbolic concentration-response relationships arise from multiple endogenous agonist molecules binding to a receptor in a cooperative manner. Thus, we developed operational models of agonism in systems with cooperative agonist binding and evaluated the models by simulating data describing agonist effects. The models were validated by analyzing experimental data demonstrating the effects of agonists and allosteric modulators at receptors where agonist binding follows hyperbolic (M4 muscarinic acetylcholine receptors) or nonhyperbolic relationships (metabotropic glutamate receptor 5 and calcium-sensing receptor). For hyperbolic agonist concentration-response relationships, no differences in estimates of ligand affinity, efficacy, or cooperativity were observed when the slope was assigned to either a transducer slope or agonist binding slope. In contrast, for receptors with nonhyperbolic agonist concentration-response relationships, estimates of ligand affinity, efficacy, or cooperativity varied depending on the assignment of the slope. The extent of this variation depended on the magnitude of the slope value and agonist efficacy, and for allosteric modulators on the magnitude of cooperativity. The modified operational models described herein are well suited to analyzing agonist and modulator interactions at receptors that bind multiple orthosteric agonists in a cooperative manner. Accounting for cooperative agonist binding is essential to accurately quantify agonist and drug actions. SIGNIFICANCE STATEMENT: Some orthosteric agonists bind to multiple sites on a receptor, but current analytical methods to characterize such interactions are limited. Herein, we develop and validate operational models of agonism and allosterism for receptors with multiple orthosteric binding sites, and demonstrate that such models are essential to accurately quantify agonist and drug actions. These findings have important implications for the discovery and development of drugs targeting receptors such as the calcium-sensing receptor, which binds at least five calcium ions.