Yes, you can run two contests simultaneously on the same Facebook page. In order to do it, you must publish each of them in an independent tab.
For each version - Basic, Premium and White Label-, you have up to 3 independent tabs to manage and organize your promotions. These are the applications of each Easypromos version:
If you want to install the promotion on a tab in Facebook, use "Quick install".
The platform will warn you if there is already an active promotion installed on the tab, and will recommend you to install it on a second tab. If this second tab is also occupied, you will be able to see if the third tab is available.
If you need more than 3 tabs of the same version on a Facebook page, you can choose one of the following options:
1. Present all the promotions in a Group, and you will only to need one application.
2. Publish the following promotions by using "Advanced install". (Available in Premium and White Label promotions).