MonoGame is designed to simplify the transfer of your game to other platforms, you do not need to use any other framework to achieve this. However, it is not as simple as recompiling the code for each new platform.
For the most part, all of your code will remain the same, but you need to build a project for each platform and link all the code files in each of them. I will not go into details about this, but I will just say that you can do it, and it is not so difficult.
Now you will find that you may have to write some specific code to process specific devices, such as screen scaling and input processing. What you need to do will depend on your game, so I cannot explain it in detail either.
To make your life easier, it’s useful to think about how your game will work on other platforms and write down your code accordingly. For example, touching a mobile device is very similar to a mouse click, so you can wrap this function in your own method to minimize code changes needed when porting. On the other hand, some things you can do with the mouse just don't work on touch interfaces, such as right-clicking and freezing. Similarly, touch interfaces have widely used gestures that do not really display the mouse on a PC, like a long press, swipe and pinch.
So, the short answer: you do not need to do something special, but you should at least think about it if you plan to transfer your game in the future.