Is it possible to have more than one corresponding author for a conference or journal paper?
Useful question about corresponding authors:
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It is possible, and at least in my field (chemical engineering) it is quite common. One example: in this paper there are two authors, and both are corresponding authors! There are even papers with more than two corresponding authors (3 and probably more)
Probably the most typical case is when you have two (or more) teams collaborating. If you have an experimental and a theoretical team, you can imagine that questions/discussion concerning each aspect of their joint paper might be better directed at the respective team’s expert. Same thing if you have a paper including very different techniques/methods, or multidisciplinary paper with teams from different fields.
Being corresponding author does not primarily concern the journal publishing process. The role of the corresponding author is to handle communications with other researchers once the paper has been published, to respond to questions concerning the research as a whole, methods, results. It is typically the most involved person who takes on this task and in many cases it is implicitly understood it is the first author. So for you to take on the corresponding author task means much more than the communication during the publishing process.
I can see reasons for there to be more than one corresponding author, although I have never encountered it. This would be if the paper contains material where two (or more) authors are experts on separate parts and it is necessary to contact each for specifics on their specialty. As I said, I have never seen it and am not sure it has ever been done. Perhaps we might find out through comments to the answer...
Having two (or more) corresponding authors is also common, if the paper is submitted by a student (or post-doc) who is expected to leave the research group soon and may not be able to attend to correspondence, reviewer queries etc, particularly in case the review gets delayed. In these cases, it is customary for the adviser to add his/her name as the corresponding author
It is possible, as far as the journal allows it. In the journal I copy edit, only one corresponding author is allowed. Full stop, no discussion.
Different journals have different policies, some, for instance, do not have the notion of a corresponding author at all, and only mention that "at least one e-mail address shall be provided".