I did add to a quilt once. the woman who asked me this had sent it out to be quilted and somehow, a border that should have been attached was not...so, I took off the binding, added a border that I had already quilting, sewed together with a 1/4" seam on the front, sewed the back side down by hand like you would do with quilting in pieces then re-bound it. When it was done, no one could tell that it had been "altered" so to speak. it's a pain but if it makes you the quilt you want, then the pain is well worth the effort.
Laurie