Is it possible to implement a windows store/metro app that represents something like a MDI(Multiple Document Interface) style application? If so what are possible approaches I can follow? I am new to the WinRT environment.
Classic MDI has been largely replaced by tabbed interfaces as in web browsers. Metro apps don't usually use these because there is no built in control for that and a GridView is the approach that handles similar problems. That said you still get Metro versions of Chrome and IE that do full-screen tabs that you could get inspiration from and then you could do a tabbed interface similar to the Zune Software which basically is a metrofied version of the TabControl.
Depending on which language and framework you use for UI development in WinRT (HTML5, WinJS, XAML, DirectX etc.) you would of course implement it differently.
In XAML you could use a horizontally oriented StackPanel with RadioButtons using TextRadioButtonStyle for tabs and depending on desired effect - use GridView/ScrollViewer (with HorizontalScrollViewerStyle)/FlipView/ContentControl/Frame/Grid or any other content presenter to display your document. If you really need to display multiple documents on screen - you could use a Grid with GridSplitters (there is no GridSplitter out of the box, but there is a CustomGridSplitter in the WinRT XAML Toolkit library), implement your own Windows or do something custom like the Toolbox app - all depending on what you want to achieve.