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can we cover ceramic tile flooring with some type of hardwood
or some other type of flooring without removing the old tile
If it were me, I wouldn't put the new floor down without removing the old one. You can rent tile removers that make the job a little easier and you'll get a better job of it, in the long run. That being said, it's possible, if the floor is very level (which would be a stroke of luck), you might be able to use one of the glue down floor systems, on top of the tile.
Keep in mind, the new system will be reliant on the subsurface being very flat. If any of the tiles sticks up above the others, it may make a "bump" that the new flooring system might not like and you've got a problem. Flooring doesn't flow over bumps very well. The middle of a job like laying the new floor isn't the time you want to have this problem.