I did this years ago. My quilt was hand quilted and when I washed it, it shrunk so much that I added 4 inches on each side.
I had the binding on and just attached a sandwich (fabric~battting~fabric) putting it on like a 4" binding.
It lasted many years, I had to hand quilt the large binding.
I used the same fabric as the outter border so it all worked.
Maybe, if you have to add 4" all around you could take 8" of fabric, fold in half put in the batting between the layers.
Just do some simple quilting, such as cross hatching.
the raw edge, that would hook up to the quilt, fold over and make it like your normal binding.
this may work!
Enjoy.
Sue