Our green marble floor has never looked very shiny in comparison with the black marble in our bathroom. Can it somehow be given a very deep shine like the other marble?

It depends on what kind of green marble you have. I would guess that the green marble in your bathroom is an Asian green. If this is the case, you will never get a deep shine on this marble. These stones characteristically have a clouded shine. If, on the other hand, you have a Vermont green or something similar, it may need to be polished.

TIP Be careful with honing and polishing green marble. Water has a tendency to cause spalling and possibly warping of the marble. Use as little water as possible.