With Windows 10 Build 10130, Microsoft added a new feature where it is possible to open multiple instances of a Modern Windows 10 app. In order to do this, you need to make sure you have the latest update to the Windows 10 Calculator app (version 10.1505.29000.0). According to Neowin, the Windows 10 calculator app is the only app that you can run multiple instances of at this time. However, according to Neowin's unidentified Microsoft source, more Windows 10 applications are sure to follow.
At the moment, the only way to open multiple instances of the calculator app is through the Start screen; if you try to open the calculator app through the Taskbar, it won't work. Allegedly, Microsoft will allow multiple instances of third party apps as well. The ability for multiple instances of a Windows 10 app will likely be limited by the developer. I imagine Netflix doesn't want you to be able to have more than one instance of their app running at a time.
It would be nice to be able to run productivity apps like Microsoft Office or Excel in multiple instances. There's no timeline on when we will see this functionality come to Windows 10, but I am sure it will be implemented in a new Windows 10 build or with the official release of Windows 10 coming July 29th. So stay tuned for more information on this Windows 10 feature when it becomes available.