Is it better to remove existing floor before placing new one
That is a common question from my customers over the years. Although it is usually better to start from a solid base of hardi-backer or concrete board subfloor, tile can be laid over an existing floor if some condition are met. 

The existing floor must be sound, with absolutely no loose or compromised sections. If your marble floor is real stone and solidly adhered to the subfloor, it can be a good base for new tile.

You need to have clearance for the extra height of the new tile. Consider things like door jams, cabinets and appliance clearances. (especially the dish washer)

Your existing floor needs to be flat without humps and ridges. 

Confirm that the marble surface will hold embossing and/or tile mortar. High polished marble surfaces may not be a good base unless dulled and embossed. Any and all sealers and wax must be removed. any grout lines should be leveled to tile, not recessed. 

As always, if there is any doubt about using an existing floor as a base, consult an expert for an evaluation before proceeding. Tile over a firm, solid can work well, but if the existing floor is not really solid, you will be wasting a lot of time and money.  If there is any question, remove it, put down a good base and start fresh.