can you? yes, you can do what you want with your quilt. And does it matter in the long run in any way? No. In trying to reduce my stash and not buy any fabrics, I have grown to love piecing my backs and making them a quilt in their own right, a la Gees Bend, if you will--making do with what I've got. One I did, I simply cut 20" blocks and sewed them together. I though "eh, not bad..." Friends oohed and aahed over the back. So, there are many tastes and many ways to do what you want to get the finished quilt (and done is better than perfect)

You could piece the backing like this.

Jan in VA