In their paper the authors investigate alternative stable states in theoretical multi-species communities. They identify 4 qualitatively different alternative stable state regimes, namely global bistability (where either all species coexist or no species survives), mutual exclusion states (where one species dominates over all other species), cliques (where a few species coexist in a group like structure, different cliques “compete” with each other) and local multistability (where coexistence of each individual species is largely independent of other species). I find the research idea quite interesting and the results sufficiently simple to understand (i.e. the authors presented the complex matter in a very pleasing and understandable way).
Major comments:
1. The paper sets out to find an understanding of how ecological systems can transition relatively abruptly from one state to another. From what I understand you identified 4 different states, as I’ve summarized above. Of these I would claim that both mutual exclusion states and global bi-stability are largely un-realistic, i.e. artefacts from the simulation. Specifically, we rarely observe monocultures nor seems a complete collapse of the system to be realistic. This leaves us with essentially two, none of which correspond to the abrupt changes you talk about in the introduction. You do mention this yourselves and state that these abrupt changes are likely rare events, i.e. local multistability and cliques may indeed be more frequent. Yet, the question somewhat remains, where in your model are these (realistic) abrupt changes? Would a slightly more complex model be able to recover these, e.g. make global bistability less dramatic where only maybe 80% of the species go extinct? Or would you rather say that this is a different regime altogether?
2. Your model includes an Allee effect for all species, which I doubt is very realistic, but that’s a minor point. However, what if Allee effects are rare, do these patterns then disappear? Specifically, I noted in Figure 4D, the LV model that we only observe cliques and mutual exclusion, notably LV models lack an Allee effect. So how essential is the Allee effect to your results? Would it be fair to say that multistability arises from alternative stable states in few-species communities?
3. Given a natural community, how can I understand in which regime I’m in most likely? One way would be to compare the fraction of coexistening species as you point out, however in nature I rarely have this information. As indeed, the excluded species are excluded and not there. If I have to investigate the regional species pool, then the obvious question is at what geographical scale? Is there a way to distinguish between cliques and local multistability from only a time-series? E.g. would we expect a correlation between extinctions and invasion in one, but not the other regime?
4. This is a technical comment where I’m not sure whether it will lead somewhere, but I wanted to mention it because I’m curious. If you find that this does not improve your paper feel free to not make changes according to this idea. You show that the number of alternative state depends on mean(A) and mean(B). But similarly, the species richness will depend on mean(A) and mean(B), and therefore the possible number of states is indirectly determined by mean(A) and mean(B), where the most states are possible if species richness is intermediate. So of all these possible states how many do we effectively observe? So how does mean(A) and mean(B) affect the probability to observe a possible state (instead of the currently shown observed number of alternative stable states).
Minor comments:
Equation 1: I know that such a function is usually assumed in order to avoid facilitative blow-up. But how realistic is such a model actually? Also, it is not directly clear to me where the Allee threshold is, could you state this explicitly?
Line 98: I doubt stating that this is an Erdos-Renyi graph helps the average reader of this journal, I think first stating what it is and then maybe in parenthesis the name might be more helpful.
Line 104-109: How do these parameters compare to realistic parameters? I think this is extremely important as this shows which regimes we should actually expect. For a review of empirical parameters you could consider Spaak et al 2021 (https://doi.org/10.1111/ele.13877) or Adler et al 2018 (10.1111/ele.13098)
Line 113: For many of the parameter choices the number of stable states is close to s, indicating that you essentially do not know how many stable states there are. Would you say such a knowledge is not important?
Line 115: Obviously I do not expect this to change the results, but why do you only include relatively low densities, why not also include really large starting densities?
Line 163: Aren’t there more than 2^N possible states? The equation are non-linear so I would expect multiple possible solutions for a given community composition (at least in principle). At quick glance the polynomial quadratic in each of the N variables, leading to 2^N possible solutions for N species present.
Figure 1: I think you should try to improve the conceptual graph. You investigate many things so why not help the reader a bit more. After reading the methods I was somewhat lost on what I should expect.

I thank the authors for their changed manuscript and having addressed my concerns as well as my curiosity. I think especially the new box 1 and figure 5 are a great addition which can help futur empirical work.

One minor thing I'd like to add is that I would say driving one species to extinction is a major empirical challenge which may often be impossible or unethical to do in a natural community. This does not undermine your box 1 or figure 5, rather I'd suggest you add a hint into that direction.