The quenching of NOA2Σ+ with O2 as a collisional partner is important for combustion and atmospheric processes. There is still a lack of theoretical understanding of this event, especially concerning the nature of the different quenching pathways. In this work, we provide potential energy surfaces (PESs) of 20 electronic states of this system. We computed the spin-doublet and spin-quartet PESs using SA-CASSCF and XMS-CASPT2. We find two potential quenching pathways. The first one (Q1) is a two-step orientation-specific process. The system first undergoes an electron transfer (NO+X1Σ+ + O2 -X 2Πg) at short distances, before crossing to lower neutral states, such as NOX2Π + O2a 1Δg, O2b 1Σg +, O2X 3Σg -, or even 2 O(3P). The second quenching pathway (Q2) is less orientation-dependent and should be sudden without requiring the proximity conditioning Q1. The Q2 cross section will be enhanced with increasing initial vibrational level in both O2 and NO. It is responsible for the production of NOX2Π with higher O2 excited states, such as O2c 1Σu -, A'3Δu, or A 3Σu +. Overall, this work provides a first detailed theoretical investigation of the quenching of NOA2Σ+ by O2X 3Σg - as well as introduces a weighting scheme generally applicable to multireference, open-shell bimolecular systems. The effect of spin-multiplicity on the different quenching pathways is also discussed.