No, only 1 Infoset chat widget can be active on the same page at the same time.

However, you can dynamically add or remove chat widgets and show a different chat widget depending on the behavior of your visitor.

You can dynamically remove a chat widget from your page with InfosetChat('shutdown'),
and you can show the chat widget you want to your visitor with InfosetChat ('boot', {widget: {apiKey: <api_key>}}).