Hi, the pre-chat questions are defined at a queue level. So, one way you can implement this is to have a anonymous queue and a logged-in queue. They can have all the same settings, so all agents can service both. When you include the Chat snippet on the separate pages, you can define the queues to use on that page.
Hi Rajesh, if you remove that setting completely, the chat will ask the customer to select from all the queues that are currently staffed before putting them into a queue. Putting multiple queues on the same page doesn't make sense, as there's still confusion as to which queue the customer would be put into.
If your question is : specify multiple queues on a page and the customer would be put into the first available slot in any of those queues, then the answer is no. That functionality is not possible.