Left: time-averaged isotropic-equivalent accretion luminosities () in LMXBs/IMXBs with a 1.3 M_⊙ NS accretor that reached an instantaneous luminosity above 10 L_Edd. These luminosities were calculated based on Eqs. (9) and (10) for each binary and at each time-step, and averaged over the entire RLO lifetime. Grey colour denotes the sequences that never achieved an instantaneous luminosity above 10 L_Edd. The systems that reach the highest accretion luminosities correspond to unstable systems, on the higher donor mass ends in both panels, before the onset of dynamical instability. The stable systems (enclosed by the solid black boundary) have a relatively low accretion luminosity on average. The magenta star corresponds to the binary shown in Fig. 5. Right: same as left but for LMXBs/IMXBs with 2.0 M_⊙ NSs. The three red crosses correspond to systems that terminated due to numerical issues.