I have done a quilt somewhat as you are talking. I had made a throw size that then the recipient requested it wider for a bed. I removed the binding and then added the width needed to both the top and the back. The only "hard part" was to get the batting in but that can be done by hand by butting the needed batting to what is in the finished quilt. Those can be pretty loose stitches just to hold it together until the quilting is done.
In fact, I recently did a quilt like that in that I needed to piece the batting. I decided it was a lot less to mess with by doing quilting up to the place of needing the batting. Then I hand basted the needed batting in place and went ahead with the quilting.