You can accept up to 10 multiple chats while your Agent Status is set to Busy - Chatting, depending what your maximum concurrent chat sessions setting is set to in the Admin Portal.

If your account is set to accept multiple chats, and you currently have a chat session in progress, when a new chat is requested from the queue you will be presented with that new chat that you must automatically accept; a new chat window will flash at the bottom of your monitor, click the new chat window to activate the chat session and enter a greeting message to begin the chat. You will be presented with chats until your maximum concurrent chat sessions are reached.