This paper is thorough and the experiment is well-designed. The inclusion of multiple conditions and an intensive training process makes this paper rigorous and informative. I would recommend this paper for publication with a few edits and clarifications.

My main critique is that the specific role and potential interpretations of the four conditions (especially in the context of the training procedure) could be better clarified. Each of the four conditions acts as a check to eliminate possible lower level explanations, so each condition is acting as a control for a specific aspect. Although the purpose of the control condition (non-visibility test) is clearly explained, the role of the other conditions could (1) be better introduced when the conditions are introduced and (2) be more clearly discussed in the discussion. Specifically, it would be helpful to have an explanation about what each condition adds to the overarching argument. It seems to me that the delayed pressing condition is the condition of the most interest because a dog could not learn to wait to press the button in the delayed pressing condition from any of the steps of training. In contrast, dogs could learn how to delay their button pressing from the training steps for the other experimental conditions. For instance, in the delayed partner condition the dogs could have learned to wait for the partner in Step 2 of the training. Most crucially, a clarification should be made that the delayed button condition is identical to step 3 of training and the dogs should have learned to wait to press the button in this condition during step 3 of training. More specific suggestions are below.

36 - Perhaps better clarification about the theoretical implications about recognizing need of partner vs. taking partner’s actions into account. It is not quite clear what different processes those two levels would require based on the wording in this sentence.
63,71 - Twice the authors mention dogs recruiting a partner, without specifying what this recruitment looks like in dogs. It would be nice for a behavioral description of this.
90-91 - Here would be a good place to explain how each of the conditions works to add to the argument, or control for specific factors.
143 - Here it should be dog’s not dog.
166 - I realize there is additional information on the training in the supplemental materials, but there are a few things that could be clarified further in the main body of the text. Here more clarification is needed on Step 2 of training, particularly how simultaneity is determined in the training conditions, and if it is different from the test conditions (which were determined by a 2 second window around the human pressing the button). Additionally, the criterion for passing each step of training should be included here, as should the average blocks to reach criterion.
175 - At which point were sunglasses introduced? Current wording suggests that addition of sunglasses and curtain is a step 4 of training.
186-187 - Specify what each condition is adding to the argument, and that Delayed Pressing is the most compelling condition, with the others being more like different types of control.
210 - It is not clear which time period or condition this sentence refers to. Clarification would be helpful.
211 - It would be helpful to include a photo of the curtain and sunglasses to clarify why it was necessary to have both the curtain and the sunglasses.
239 - Why are only variable delays in this matrix? This could be further clarified in the manuscript.
244 - Edit GLMMs - should be plural
262 - Here the authors refer to “pressing the button”. Earlier they clarified that “success” was marked by pressing the button within two seconds of the partner. Here, it is unclear if they are referring to pressing the button within 2 seconds of their partner or solo pressing of the button (irrespective of the partner’s pointing).
289 - This does not seem to be that high of variability. Perhaps take out the word “high” before between-subject variability..
328 - May need the word “only” else there is a typo.
333 - Replace intricate with “complex” which may be more appropriate.
335-338 - This sentence is confusing and could be reworded.
359 - Should be “In consonance with” rather than “In consonance to”

The authors thoughtfully addressed all of our major critiques. We have only a few copy edits to make before recommending this article for publication.

132 - what is the 37? A citation or number of errors?

225 - The sentence ends with "avoid" when it should have a direct object. It seems the word "tiredness" was deleted.

353 - 354 missing closed parentheses

390 - Dogs should be lowercase, as it is the second word in the sentence

433 - "and their" appears twice in a row