You can do this, I have done this for my game Tokyo Hosto for the following platforms: - iOS - Android - Windows Phone - Windows 8 Metro - Xbox 360 - OUYA - Playstation Mobile
I first created the XNA projects, coded them to about 90% and when there was a lull in development (because I was waiting for animation to be sent to me) I started work on a MonoGame port. I didn't do anything particularly clever, instead of copying in my source files I linked them in. This meant there was a single set of code used for each platform.
I simply used compiler directives to iron out the platform specific details.