You can have multiple games running simultaneously. These can be of the same quiz or multiple quizzes.
To create multiple games, just go to the relevant quiz page and click "Play Live" or "Homework" to create the first game.
To create the next game, just go to the quiz page again, and go through the same process by clicking "Play Live" or "Homework". This time a new game code would be generated.
This way you can create as many games as you require, there is no limit. Each game will have its own separate report.
Note: You don't need to keep the browser tabs open for the game to stay running. To see all your running games, just go the "My Reports" section and go to the "Running" games tab.