Getting them to line up might be a bit of a problem I could imagine if you were to program it directly. 

Here is how you'd get the very basic axes down:

From here there's a number of things you could do. Working directly with the graphics primitives would probably be difficult. The other option is to try to do something tricky with the Ticks option and give it some unique labels for the tick marks. Here is how we can generate tick labels:
So here are the positions and the labels together as pairs:
And we can use them in the graphics like this. 

Can you give an example of the kind of plot you want? This will help make sure we understand exactly what you want.

Are you looking to add a new axis in your plot that's next to the X axis? There isn't going to be a built-in option for this. For things this custom, it is neccessary to build them up from graphics primitives such as Line and Text elements.