G-protein coupled receptors (GPCRs) are a versatile, important class of cell-surface receptors. GPCRs occur in different conformations that exist in a dynamic ligand-sensitive equilibrium. These conformations vary in their affinities for intracellular signalling proteins and initiate signalling via different intracellular routes. The binding of extracellular ligands and allosteric ligand-ligand interactions shift conformation equilibria to cause biased signalling. Here, we present a mathematical model that describes the effects of ligands on the conformation equilibria of GPCRs. Our extended Monod- Wyman-Changeux model describes the receptor as shifting between active and inactive receptor conformations under the influence of extracellular ligands. For each receptor conformation, the intracellular domain of the receptor can attain alternative domain conformations that differ in their affinity for intracellular signalling proteins. At the extracellular domain, the model can accommodate different mechanisms for allosteric ligand-ligand interactions that induce shifts in receptor and domain conformation equilibria. We use the model to study ligand-biased signalling and how ligand affinity, ligand sensitivity and maximal signalling output depend on allosteric ligand-ligand interactions.