Activation of the G protein-coupled receptors by agonists may result in the activation of one or more G proteins, and in the recruitment of arrestins. The balance of activation of different pathways can be influenced by the ligand. Using BRET-based biosensors, we showed that the vasopressin V2 receptor activates or at least engages many different G proteins across all G protein subfamilies in response to its native agonist arginine vasopressin (AVP). This includes members of the Gi/o and G12/13 families that have not been previously reported. These signalling pathways are also activated by the synthetic peptide desmopressin and natural homologs of AVP, namely oxytocin and the non-mammalian hormone vasotocin. They demonstrated varying degrees of functional selectivity relative to AVP, as quantified using the operational model for quantifying ligand bias. Additionally, we modelled G protein activation as a Michaelis-Menten reaction. This approach provided a complementary way to quantify signalling bias, with an added benefit of clear separation of the effects of ligand affinity from the intrinsic activity of the receptor. These results showed that V2 receptor is not only promiscuous in its ability to engage several G proteins, but also that its signalling profile could be easily biased by small structural changes in the ligand.