Framing over ceramic tile?

We have a room that is currently carpeted that is open to the tiled hallway with @ 95" wide opening. I'm wanting to frame a wall and install afrenchdoor. Rather than cutting the tile where the new 10" walls would be framed can I frame over the tile? I am trying to keep the carpet / tile juction near the center of the door jam and am trying to avoid having to cut and remove any tile. Thanks

Don't see why not. Probably not the best idea but do-able I suppose.