Can I have multiple backlogs in the same project?

Yes, you can have multiple backlogs in the same project, each with its own backlog lists. For example, you could have a backlog per subproject, application module, or client:

To add a backlog, click "Edit this backlog" at the bottom of the Backlog tab, and then click "Or, add another backlog". If your project already has multiple backlogs, instead click "Manage backlogs" at the bottom of the Backlog tab.