There is no reason why you should not do this.
The chimney is around 9 inches deep, so with bricks and plaster you should gain about 15 inches.
However, you must seal the top of the chimney to stop the rain and cold air dropping down. And seal off the chimney just above the set, to avoid soot dropping into the set.
Once this is all done, you then have the problem of a cold chimney in the middle of your room.
Because its cold a lot of the humidity in the room will find its way into the chimney breast.
Because the chimney hole is 9 inches wide a convection current will start up inside the chimney moving the heat and moisture from the room to the other side of the chimney.
Please see our projects on opening and closing chimneys. A chimney stack needs to remain ventilated at all times and removing sections of it at any time may well affect the integrity of the rest of the stack above it. Your stack is carrying weight of the stack above it right up to the pot on the roof so pulling it apart may not be a great idea until you have had it looked at by a pro.