Examples of fiber cement board.
Cement over tile floor.
Examples of cement board are.
Lightweight cement based overlays mimic stone brick and other wall textures placing overlays over tile floors by chris sullivan chemsystems inc.
You most certainly can pour a new floor over your ceramic tile.
Wonderboard durock and permabase.
These come in two categories.
Another and i think better way would be to use a self leveling concrete that can be aplied in a much thinner coat and if head room is a problem would be of help.
If you were to use conventional concrete i would say you should pour a minimun of 3 inches both for strength and to ease leveling.