Nature Communications has had a policy since 2016 that authors are given the option to publish the peer review history of their paper.
Are there other journals with the same initiative?
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The publisher Cooernicus has an open peer-review process, i.e. all peer-reviewer reports as well as the answers of the author(s) are published open access.
The peer reviews for several highly regarded machine learning conferences (most notably the ICLR - International Conference on Learning Representations) can be found at https://openreview.net/. While these are not 'journals' in the strictest sense, they do have a peer-review process. The setup is however double-blind.
The website, e.g. for the ICLR allows you to do the following: