Is it possible that i make extra axis lines to display information during drawing a 3D surface plot

[#1]

During i draw a 3D surface plot like this, i can add only 1 line on each axis (x,y,z)

So i'd like to know whether i can utilize extra lines on 3D surface plot.

And if possible, please let me know how to make it.

[#2]

@BottleCollector , are what you wanting to do is create a graph like what is shown on the left, sometimes called a 3D waterfall plot?  

[#3]

I want to add extra lines on the 3D plot like blue lines on this screenshot.