How to configure maximum IMAP connections in Mac OS X Server (El Capitan)?
You should be able to increase the number directly in the respective config file:


Stop the server:

sudo serveradmin stop mail

Modify the file /Library/Server/Mail/Config/dovecot/conf.d/20-imap.conf and increase the number of mail_max_userip_connections right at the end of the file:

...
protocol imap {
  # Space separated list of plugins to load (default is global mail_plugins).
  # stats (in global mail_plugins) and imap_stats (here) are also available
  mail_plugins = $mail_plugins imap_acl imap_quota imap_zlib

  # Maximum number of IMAP connections allowed for a user from each IP address.
  # NOTE: The username is compared case-sensitively.
  mail_max_userip_connections = 20
}

Start the server:

sudo serveradmin start mail



Other (Linux) sources recommend to add a similar entry in the global section of the same file or in /Library/Server/Mail/Config/dovecot/dovecot.conf.