I have sewn 3 borders together than added to quilt and mitered...turn out perfect.

I usually sew the border strips together and treat them as a single piece of fabric.

I've done it and it worked just fine. Figure out how much extra length you will need for your second border. Don't sew the borders together right to the end before applying to the top. I didn't use either a mitred corner or cornerstones but just partial seams until everything was attached the way I wanted it and then finished the seams. It was a bit fussy bout way easier than attaching them one at a time for me.