Dear authors,
thanks for your interesting paper. The critics calls for moderate revisions. Please follow the lines of arguments as outlined in the answers to the referees.

Dear authors,
the manuscript has improved and requires only minor revisions.

1) please follow the suggestions of the referee, and provide a point-by-point answer to the comments.

2) My own evaluation and following comments can improve the quality of the paper.

a) page 2, lines 25-28: Referencing to double well potential and dynamics of abrupt climate shifts. I think the method and application of Livina and others were first described here: Kwasniok, F., and G. Lohmann, 2009: Phys. Rev. E, doi: 10.1103/PhysRevE.80.066104

b) I think that the statement
"1 This algorithm has been implemented in many software packages."
could be avoided as footnote. You could include this statement in the full text and provide references.

c) section4, lines 270ff, 282 ff. The Langevin model is a simplified view and many features like the gyres are missing. In Prange et al. (2003) it has been shown that even 2D and 3D models can have a substantial different dynamics because of the missing dimension. I guess that this is even more true for the 0-d model. In 3 D models, a reversed flow as off mode does not exist (see e.g. on Fig. 9 of their paper) due to the gyres (section 4b). THis might be also related to your statements lines 250 ff on page 13, and lines 260 ff on page 14, lines 274 and 283 on page 275. The salinity advection mechanism is indeed not the mechanism for the off state. If feel that the speculation with the metric (lines 284-286) could take this into account. The way it is written now is somehow misleading.

d) page 17, line 322: This statement is not correct: "it is not clear how long the models in Rahmstorf et al. (2005) were integrated per freshwater forcing value". This value is given in the paper. "The rate of change of the freshwater input was 0.05 Sv per 1,000 model years." This information could be easily included.

e) page 18, lines 327 ff: The statement "As noted by Gent (2018), the hysteresis behaviour has not been investigated fully in models of greater complexity than EMICs" is probably not true. See some examples by Mikolajewicz (with a higher freshwater rate in the hysteresis) and other colleagues like Zhang in 2017. Just reformulate.

f) page 18, line 337 ff: In coupled models M_ov is just describing the oceanic feedback, it implicitly assumes that the circulation within the Atlantic is a second order effect. In truely coupled atmosphere-ocean model is seems that the atmosphere has a similar order of magnitude affecting the freshwater (e.g. Lohmann 2003; Ackermann et al. (2020, GRL) and others. In this direction also the Liu et al. work is interesting that in not flux-corrected coupled GCMs the salinity bias is so strong providing a more monostable behaviour.

Congratulations for the paper!
It is also good that you used the original data from Rahmstorf et al. in the final version of the paper.