How do I change the number of connections to a mail server?

If multiple mailboxes are used by using multiple parallel mail clients running an IP address, some clients may not be able to connect to the server.

FOR THUNDERBIRD:

In this case, under Tools / Account Settings, select the Server Settings under the mailbox.
Click the Advanced button, then in the Maximum number of server connections to cache, reduce the set value to 1, and then click OK.