I re-quilted my daughter's quilt when it fell apart after many years. I cut off the tattered binding, layered a new backing right on top of the old one, machine quilted the whole thing (it was originally hand quilted) and then put on a new binding. All the fabric, both in the original quilt and in fabric added, was pre-washed, so there was no problem with shrinkage or any other issue. She was very happy that I could give new life to her old favorite. So, go for it!