Problem
In a community, a moderator felt that a user had violated a community norm, and so the moderator suspended the user. The user strongly disagreed with the moderator decision and furiously vented his/her anger over it. Should the user be punished again for the venting?
What the moderator may do
This depends on the established rule/norms of the community. If there is a community rule explicitly asking members not to offend others anywhere within the community and moderator communication takes place within the community, then the moderator could take additional disciplinary actions (such as suspension) specified in the written rules for such a code of conduct violation. In this case it is recommended to explain to the user why and according to what rule such a decision is made.
But, if there is no rule required for dealing with such a situation, it is recommended not to take additional disciplinary actions not endorsed by any established rule.
What the moderator should do
Instead of prescribing a remedy for the problem, I mention the following points so that regarding them would be helpful when dealing with such a situation.
First, seeing that the user strongly disagreed with the disciplinary action, should the moderator not think that there could be a (faint) possibility that the decision was wrong? So it should not be a bad idea to reconsider the decision; reconsideration should be done by other moderators (if any), and/or it could be done by the community if need be and the user's approval of revealing required information be given.
There will be two cases. If the decision turns out to be wrong, it should be retracted, and the moderator should apologize to the user for it. On the other hand, if the decision turns out to be right, it will become more justified, which would help the user become calm and confident.
Second, unlike some people believing that the moderator should overlook such a venting expression, I think that ignoring a user who is very furious over a moderator decision does not seem constructive.
The user in question claimed that he/she already moderated many communities and so was well aware of how to make proper moderation decisions. In order to make the decision more justified to the user, the moderator could ask the user to explain how he/she as a moderator of a community would handle such a situation. So after a constructive talk about the matter, common points between the moderator and the user would likely be found so that the tension becomes less severe.
Third, the last but not the least, to answer the question of the OP from another point of view, let me begin with asking some questions. What is the purpose of (recursively) punishing the user? Does the moderator really expect that after the suspension the user would come back to the community expressing remorse for his/her past behavior like "I feel sorry. I should not have done that. I promise you to behave properly"?
Unfortunately, many community moderators are too impetuous and willing to punish bad members. Even regarding correct, justifiable disciplinary actions, I think that most of them can be avoided. In my opinion, moderation is more an art than a science. Moderators must have and use authoritative privileges to manage their communities well, but a wise moderator will not put their effectiveness easily by overusing them; "the ideal moderator does as little as possible."
So, let me conclude this answer by this comment: You could punish and repunish the user; however, please keep in mind that in almost all cases there tends to be an inverse relationship between using power privileges and the value of what is gained.