In 3rd party desktop chat clients like Pidgin or Adium or 3rd party mobile chat clients like AstraChat or Xabber, operators will follow the chat management link that comes in at the beginning of each chat to send a transfer. The link will take the operator to a special page for management of that specific chat. From that chat management page, they can transfer the chat to another queue or individual operator. They can also send the guest a file, email a transcript of the conversation, tag a chat for follow-up, use the sharing tool, or block abusive guests.
Example chat in Pidgin:
Chat management page for external chat clients: