Short answer
Yes, you can switch to a different Index during a chat in AskTuring.
Full explanation
While you are on the Chat Screen, you can change the Index you are using without leaving the conversation. At the top left corner of the screen, under your organization name, there is a drop-down menu listing all available Indexes.
To switch, open the menu, choose a different Index, and AskTuring will use the documents in that Index for the next questions you ask. This allows you to quickly move between datasets without starting a new chat.