Yes, you are able to select multiple reports for a specific screen.
You have a few options to do this; use a dropdown, use 1 button and add multiple events and lastly if its only 2 options you can add 2 buttons on the screen, each calling a different report.
With regards to the 1st option you can add a dropdown and add actions to check which value is selected from the list and if it is a specific value then pull that report. Clue: you'll need to use conditional statements and generate report actions.
For the 2nd option, add a button to the screen and under step 2 when editing the preferences for the button you can add multiple events, each of which would pull different reports. Hint, add actions to generate specific reports for each events. Once completed you can then click on the button and a pop up like features comes up with the different selections list (events).
The last option, is pretty straight forward, just add 2 buttons to the screen and each one calls specific reports.
Hope this helps.