How much is too much communication?

Communcation if communicated clearly and to the point should not be an issue at all. Effective communication is always essential and can't be quantified at all.

How much communication depends on the requirements, needs, and so on.

Here is why one should know the importance of Effective and Efficient communication.

Effective communication - information is provided in the right format, at the right time, to the right audience, and with the right impact.

Efficient communication - providing only the information that is needed.

Communication always is an issue in a project, that's why you should develop a communication plan at the start of the project...Depending on the nature of the project and the needs of the stakeholders you can exactly define who needs/wants to see what, how they'll get the information, how the email chains you mentioned can be prevented (e.g. calling meetings for certain issues), that for certain stakeholders any important and urgent emails will always have their assistant in cc, whatever works for you, your team and the stakeholders.
As a side note: For any organizational development project that is meant to change the behavior of people and transform the organization, I really think there is no such thing as overcommunication.

Yes too much communication can become a problem, and people might get disoriented by this resulting in missing the important communication and further delays in decision making (if expected from them after getting the message) or providing vital input to the decision making.

so to keep it crisp :

1) always set expectation before initiating a communication. I case of sending mail make it clear what is intended from it.
2) request an acknowledgement for the message. this will help you know if the message was understood and avoid delays.
3) If it's a mail chain, then summarizing the entire mail chain (on every 3-4 mail loops)in one single mail (in continuation to the mail chain for all audiences) is good practice. this will save time to go through all the mail chain for everybody in the mail loop
4) try and use common platforms like internal social media for effective communication
5) meetings are best possible ways to avoid lengthy mails and arrive at conclusions quickly.

and many more such steps.

so if you message is not fetching intended results in quick time for required stakeholders then it is too much communication resulting in nothing. stop it right there.